{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Modeling gravitational fields"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.1 Defining a vector field"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x,y):\n",
    "    return (-2*y, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_vector_field(f,xmin,xmax,ymin,ymax,xstep=1,ystep=1):\n",
    "\n",
    "    X,Y = np.meshgrid(np.arange(xmin,xmax, xstep),np.arange(ymin,ymax, ystep))\n",
    "    U = np.vectorize(lambda x,y : f(x,y)[0])(X,Y)\n",
    "    V = np.vectorize(lambda x,y : f(x,y)[1])(X,Y)\n",
    "    plt.quiver(X, Y, U, V,color='red')\n",
    "    fig = plt.gcf()\n",
    "    fig.set_size_inches(7,7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_vector_field(f,-5,5,-5,5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.2 Defining a simple force field"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(x,y):\n",
    "    return (-x,-y)\n",
    "\n",
    "plot_vector_field(f,-5,5,-5,5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Adding gravity to the asteroid game"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See asteroids.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EXERCISE** Where do all of the vectors in the vector field $(-2-x,4-y)$ point?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def g(x,y):\n",
    "    return (-2-x,4-y)\n",
    "plot_vector_field(g,-5,5,-5,5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3 Introducing potential energy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.1 Defining a potential energy scalar field"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def u(x,y):\n",
    "    return 0.5 * (x**2 + y**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
    "\n",
    "def plot_scalar_field(f,xmin,xmax,ymin,ymax,xstep=0.25,ystep=0.25,c=None,cmap=cm.coolwarm,alpha=1,antialiased=False):\n",
    "    fig = plt.figure()\n",
    "    fig.set_size_inches(7,7)\n",
    "    ax = fig.gca(projection='3d')\n",
    "\n",
    "    fv = np.vectorize(f)\n",
    "    \n",
    "    # Make data.\n",
    "    X = np.arange(xmin, xmax, xstep)\n",
    "    Y = np.arange(ymin, ymax, ystep)\n",
    "    X, Y = np.meshgrid(X, Y)\n",
    "    Z = fv(X,Y)\n",
    "\n",
    "    # Plot the surface.\n",
    "    surf = ax.plot_surface(X, Y, Z, cmap=cmap,color=c,alpha=alpha,\n",
    "                           linewidth=0, antialiased=antialiased)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DdzfSCYdTq9UwOTmJRCKBc+fONV3B3v/Yv3W1HauwmhnRaBQjIyMYGRkBUG+lsr6+jrt376JQKCAej6NWq6FYLOoEqNN0w8m+G/aBEFRIzSssyyISiaguSJZldSaQcShdNptFLBazbEgKNLqCaEcyGHNA3fIZtAoVnC7HqmOAIAi4fPkyOI7TFQYEkW8JumhgbW0NV69exdGjR9U1FE6YuRwzzJyPVcUaaaWyd+9etZnkxYsXMTc3p7bTJ1e42nkuO4FuEpxOhdTcIEmSKhosy6Kvrw99fX04ePCgOhU1l8vhxo0bqFaruplA2qmogHk/ONKQ9Pd+7/dw7NgxvOtd7+r43+gnVHC6GKs+aOQEfeTIEfXqnBBE+CuoogFtp+onn3xSF4JoBy8uxwrSTDISieCxxx4DwzAol8tYX19XB4ppr16NJw8/6YaigW5xFcD2ET/tVFTjULqZmRl1KB0J4xovYrQCVCqVdDmi7QoVnC6FuBpjYcDNmzexsbFheYIOSnD8PunJsozz58+jv7/ftlO1HcTluM3faBF/79cR+r9+2/Xjte30yTwXcvK4efMmqtUqUqmUevLwSzy1r7+VbJeTfKfxsi92Q+nIRQxx0f39/bqhdOS+7Q4VnC7DqjCgVCphcnISw8PDGB8ftzz4gxAcv7d5//59lMtlHD9+XC1BtaP4n37F82v44XIIZmJrdvIoFApYX19X4/fpdFoNwW33q9OtStSbsV0Fx4jdULrZ2VmUSiWUSiX84Ac/wNramqeLmPn5ebz3ve/F0tISWJbFhz70ITz//PP45Cc/iT/8wz9Uuy98+tOfxlvf+taW9r8VqOB0EVaFAQsLC5ibm8Pjjz+Ovj77FfVBCY4fDkeWZdy4cQOFQgGJRMKV2DiRHLZ+P5ycjxuX4/YkyzCMGj4h8XsiQFeuXIEgCOoiQrKGwy3d4C66YR8I3bQv2hxOu5gNpVtcXMTk5CSmpqbw3HPP4dixY3jTm96En/mZn8GBAwcstxUKhfC5z30OTz75JAqFAsbGxvDMM88AAD7ykY/gYx/7mC/77BUqOF2AsTCAXDGRwgDt4kcnujWHQ0q3d+3ahbGxMXz/+9/39Pz4YAaV1byn5ySGB1BeWTO9PWi0CeRDhw5BlmV1EeHCwgIkSUJfX58aPnEzJmIr6YY8EqGbBCdIt8UwDPbu3Yvnn38er776Kn7nd34HHMfhu9/9LnK5nK3g7NmzR12Ll06ncfz4cSwsLASyn16ggrPFWBUGrK6uYnp62rQwwI4gKsrazeEsLS1hZmYGjz/+uK6nmx8njuTIoKmouMVrLqdVWJZVw2uHDx9WV7Gvr69jbm5O7eNFBEh7cdEtJ/tuOckD3bMvnQrvkQKDvXv34qGHHvL03NnZWbz22mt46qmn8Morr+ALX/gC/uRP/gTj4+P43Oc+5ziA0U+o4GwhJFdjLAy4ceMG8vk8xsbGEIvFPG0zqLLoVrYpSRKmp6dRq9Wahr0REXM6cbjJ31g5Gaf7thLjKnbSx2t9fR2zs7MAoIbfgK0/wXaTq+gmOpXbIlWRXikWi3j22Wfx+c9/HplMBh/+8IfxiU98AgzD4BOf+AReeOEF/PEf/3EAe2xOd2Tedhikvv7ixYuo1Wrqgq5SqYSJiQlEIhGMj497FhsgmBNTKw6nWCxiYmIC6XQaZ86caQoZtbLN+GDG9WO9hM3E3/t1T/sRBKSP18MPP4zx8XGcOXMG/f39WFtbQ7lcxoULF9SZRn6O+3ZLNwlOtzg+oLmFTVBUKhXPlY+CIODZZ5/Fe97zHrzznfXBhbt371YXkX7wgx/ExMREELtrCXU4HUZbGED6oXktDOg0Xg4o7d9y4sQJZDLmIuF3qbVbl+M1f7NVoxm0nYxzuRxOnTqFXC6HBw8eYGZmRtdmpRONSLtpHc5ORFEUT13fFUXBBz7wARw/fhwf/ehH1dsXFxfV3M7XvvY1nDhxwvd9tYMKTocwK3fmOA7VahVXr15FJBLxZZTAViKKIq5cuQIAjn+Lm1yTWThNWzyQHGm/yo3A/Omnobzn3/u2Pb8Jh8O6YWK1Wg3r6+sda0TaTQ6nW/YD6C63peWVV17BV77yFZw8eRJnzpwBUC+B/upXv4qLFy+CYRgcOnQIX/ziFzu6X9v37LaNsCoMEAQBk5OTeOSRR9S57NuVfD6PqakpHDx4EKOjo66e4/fB2q35miCIRCLYvXu3+r1x24i0VbppHU63nuSDopW/9w1veIPp8zq55sYMKjgBYtUHjRQGFItFnDhxQr1q3Y4oioK5uTncu3cPp06dcp3YbKeazqlE2ixs5iaU1u0uxw43jUiJA9KuYHdLNzmcbqGT70mvvP9UcALCGEIjX5ZisYjJyUmMjIyoCbztSq1Ww9TUFGKxGM6dO+fpb3GTG4lk+1BbN2/QaVVA0Ik1NtsBs0akpAKulUak3XLC65b9ADq3L93kLtuFCk4AmA1I045LJsn0a9eudXySpl+QFfQPP/xwS+FAp/Lt2n+xdxpsCwslI0MDqD1oDrmFBxtrg8xczlaHcNp9fdKINJFIqCvYvTYi7ZYTfbfsB9C5NTiVSqUn+qgBVHB8xaoPGnEC0WgUTz31lK6deVCCE9SBqSgKbt26hQcPHrTV4dntvlm5nHC2D4KF+/GTbjm5+YlTI9JKpaL2gSONSLdadAm90kfNC+Vy2fdmsFsFFRyfMOuDBgAPHjzAtWvXTGe9cBwXiOAQIfM7XMfzPCYnJ5HJZFru8EwIauRBZKgeUjNzMuR+q/vUfeuyXE7QouemESmZRMnz/JY2Iu0mwfGzj5odpVLJcvrtdoMKTpvYFQZcv34dxWLRsmMAy7KBLOILor2NKIo4f/48Hn30UQwNDbW9PbscjjGcttUuZ6dh1oh0bm7Ol0ak7bJTQ2pUcChqxwBJkkwLA/bs2YNHH320o6MEAH/dA5nBw/M8fuInfqKl7gdmtHPSiA47C57RyRDnY7xPm7/REv7GH0D4qV9ueR97CZZlEYvFMDg4iAMHDmxpI9Jucjg0pOYdKjgtYlUYMD8/j7t37+LkyZNIp9O22wjS4fghOJVKBZcuXcLQ0BCSyaSvV7J2osj190HKuXMunXA53ZK/2Eq0zqKdRqTt0k0VW50SHBpS28E4FQbEYjFdYYAdHMepoTg/8UNwlpeXcfPmTTz22GPIZrO4f/++rydery1j7Eqk1ccMDTT93k4uJ/yNPwCz739xvY+9jF0oy0sj0v7+/rbyHt3UYqdTOZxemfYJUMHxRCuFAXZ0o8ORJAnXrl1DtVrF2bNnVVfjd17ISnCkP/8MAGuXYxZOa9XlRIYGoCj279PZu99D6bHHPG+71/CSOyGNSMmAPVEUkcvlsLa2htu3b4NhGFV8+vr6PJ20d2pIjTqcHYRVYYAkSbh+/TrK5TLGx8c9V+8ElcNpdbulUgmXLl3C3r17cfz4cd0Jxu+qslaaYkay1k1Nwxb3GV2PFi6bhbi26mkfdirtOAttI1Kg3tKp1UakO7VogDqcHYKiKFhbW0MsFgPHceqXvVAoYGpqCnv27MGxY8daOgi6SXDu3buH2dlZy27VnXI4Wrzkcvwk1KcvJEj+3R9taQFBN+SQ/DzRt9OItJscjiRJHcvhtDILpxuhgmMDKQy4fv06jh07hkQioesdduLECcfCADuCXIfj9iRFOjwrimLb4bkTDoeE0+ywEqHQ4IClOHHZLKT1ddP7QgOD1OW4IEhn4aURaadO8m6wW+u28is/BwAY/v0/b/t1KpXKtm/uS6CCY4KxMIAIA8/zmJqaQiKR8Nw7zIygcjhuxaFQKGBychIHDhzA6Oio7QnF77kwrWwvtMu+HLpVR+RGdLayTLpbQkidwq4RaS6XA8MwiEQiLTci9QtZlm0r8PwQG4AWDfQ0ZoUBHMfhwYMHWFhYwCOPPOJbd+etCqmR8u2FhQXXHZ793le3gmMmIl6Ehdsc0WznclyRdj9ttBfZylCWthHp8vIy8vk8WJZtuRGpX1i9J8Td+EWr46W7ESo4mxgLA8gXSZIk5HI5FIvFlgoD7NgKwREEAVNTU+rAN7cuLWiHo3zjD8Cm0pCLBc/bCg167xBNhEjdxqbLMeZvtIS/+18hvOnfeH6tXqBbkvWKoiAajWJ0dLTlRqR+0anwHnU4PYbVgDRSGBCNRnHo0CHfe0hxHNfRsuhcLofLly/jyJEjarii3W22ihcB4/r7wBhWr1u5HDv307bL2cF0k+AYqye9NiL1C7Mcjt/uBqBl0T0FcTXGjgF37tzB4uIiTpw4geXl5a6pJmtlu4qiYHZ2FisrK3jiiSdaulrqhhyOV4wuxonQwCDgcAGwU11OtwiOU2jPTSNSIkDZbLati0jjvgQhNgAti+4JrDoGmBUGPHjwIBAn0okqNdLhOZ1Ot9XhOciyaOUbf9B4HYuwGpPKQClaT/nU4uRyPGPI3+xE0ekWwfG6HsisESkRoHYbkdqJn18FAwAti972WHUMWFlZwY0bN5oKA7ZDk02z7a6urmJ6etqXQoduWPhphOvvA2ORg+L6rReJWpLZzN+s0zJpI90iOE6VYU6wLIu+vj709fXh0KFDbTUi1eZwgnI3AHU42xZtYYDW1Vi1cyEElWsJ6gBmGAZLS0sAYDkaoZVtdiqkZnQ5bLbeIsWLy7GlLwtstJfL6aTL6bWFn+3gd7VcO41ISQ6n9P9+2Lf9MYPmcLYhVoUB+XweU1NT2LdvX1M7FwLHcajVap3e5ZaoVqu4ffs2YrEYxsfHfTtJBFU0oA2ntUS6Hyjkmm/vH2xdVLKD1OUY6BbBCXo/vDQiJQ6nsBxsIYooih2dORQkO0JwSK7GqjDAaS1KULkWvyEhwb179/p+YHa6aKDVEmkdZk6mL2t9nweUZAah838DcfztbeygO3bCid4tnV4PZNeIdGNjA+JnfrXpOX7mb4Du+Pz9ojt6RAQEGZCmXVvDMAyq1SouXLiAarWKp556yjEhF1RHAL+QZRlXr17F/Pw8zp49i0wm47tABlY0kHSYGbQZTlOfl2ok8Jn+zfvS1mtnXJMxbIO8rsOCz9D5v2n/tbcB3SQ4W7kfpBHp0aNHMf5dc2G5ffs2crmcL8egoihdEVL1i551OGYD0oCGC/AyKjmoHI4flEolTE5OYmRkRG0iGkSRQxBFAwdu/WP9l2QaKLXpZqywczJOLic7CIjO84pqtVrPhDys6BbB6aZ5OGYkd2ehJBKuGpF6oRveez/oWcERRRGAvmPA9PQ0eJ43LQywI+iQWqsHs1WHZ7/dCBCM4DjBpszdj2nxgDaX0z/Y/KQASVz6Fn6Avb4NGetGukVwuqVbNCkUKJnkb9w2Ik2n047vaS+5G6CHBUd70iWFAfv378e+ffs8HzhBhtRIaMnLPkmShKtXr0IURdMOz0GUW/spYrIsY2lpCXu0N5q4HCU7BMaiKo3xIirEyfSZrMEht1n8bXJmEGxeX0CgJJvDbD+Ge1jqP4S1tTXcunVLnfEyMDDQ1pVtt9BNgrPV+2FVlZbcnUXy//n/dLfZNSItFAqIx+OqAzJrRMrzvC9Vpt1CzwoO0Fhhv7y87LpJpRkcx+H+v/i3+HsA/7J4ydd9JO7J7QmJdHi2E88gQmp+bbNareLSpUs4W7rm6vFKKmMqOnIyA7Zk43KMmIkN2VaqH2yh+UpVTnhr2KkdMkZmvGivbAcGBjx3OO6WK9xuEZytDqlJf/DvTG9P7na3oFjbiFRRFFWArBqRktt6hZ4VnGq1iosXLyKTyeDcuXNtfUk5jkPfP3wJG2/+gI97WIe4J6fFbIqi4O7du7h79y5OnjxpO4enW3M4ZCHqsWPHgEsmguNHLieAcJqZyzGDufwPUB5/M4DmGS+VSgVra2vqiSWVSqknFj/7ewVFtwhOt4TU/IBhGCQSCSQSCdNGpJ/97GexsbGBUqmEmzdv4siRI64+g/n5ebz3ve/F0tISWJbFhz70ITz//PNYW1vDz/7sz2J2dhaHDh3CX/zFXyDbSueNNuiNT86E9fV1PPTQQ3j00Ufb/oJqT+B/nzrlx+6ZbtsKQRDw+uuvY2NjA+fOnXMc+haU4LR6ta0oCmZmZjAzM4OxsTG1xNT2OdnvTEseAAAgAElEQVRGQYeS0jsNua/+fNkktCWnWqtYk9PtHXhSvP6ZMJf/wfT+eDyO0dFRnDhxAufOncOBAwcgiiKuX7+OiYkJTE9PY2VlRa2oJFCH0z370a67cYI0It23bx9OnjyJL3/5y3j/+98PSZLwwgsv4PTp03jhhRcctxMKhfC5z30OV69exQ9+8AP8/u//Pq5cuYIXX3wRTz/9NG7cuIGnn34aL774oi/77YWedTh79+5VCwfahVSp/cviJd8Fx6kCbmNjA5cvX8bhw4exZ88ey8dp6aaQWq1Ww+TkJFKpFMbHx+vb+f5fAbEkmGrJ1320gwgRW7QIuTk9f9PlmOVvvKJtMHngwAHIsox8Po+1tTXcvXsXsiyrBQiZTGbHn+i1bJXDIWJTfdD4/hgLBoz5m3bhOA4HDx5UxUeSJMzPzzs+b8+ePeq5Ip1O4/jx41hYWMDXv/51vPzyywCA973vffjJn/xJfOYzzlN2/aRnBcdPjAfa36dO+ZbLsTqRa/NPZ86c8RTH7RaHQ8YhHD16FMPDw+6eZBFW85LLkVP9roVF64jkdFbN5Zjlb+TMIBjJuUxaG1pzA8uy6O/vR39/fV+0iwvJjJfbt29vaQHCThccM/xyNnZoczgcx+HQoUOenj87O4vXXnsNTz31FJaXl1Uh2rNnD1ZWVvzeXUeo4GwxZuJAXAHpWO31AAui9b+XKjXSxWFpacl2HIJi4XK04TQvkFCb7WM8iFE7eBUdLWRx4dDQECRJwo9+9CMkEom2CxDaoVsEZyv2wyqU1gna6aNWLBbx7LPP4vOf/zwyme6YWNuzghPUl9LvsJpRcNbW1nD16lVvrsBhm37gtmiATBSNRqOmYil//68ctyHH02Ar5i5H4Zq797brcnTP07gcM8T0IEIFfQEByd8EBcuyrgoQBgYGAiuh7RbB6bTDcSs2fofTCK12ihYEAc8++yze85734J3vfCeA+vqgxcVF7NmzB4uLiy2fX9qhO7zpNsQv0SE5HEVRcPPmTdy8eRNjY2NtfRm2KqSWz+fx6quvYmRkBI899pirE4MSC74LrrGQwKmwwKqAQNoMs4lpd5Vw8o0funqcHWbvuVUBwrVr12wLENrdj24QHKBzq+7ZP9fnN7T5m05RKpU8OxxFUfCBD3wAx48fx0c/+lH19re//e146aWXAAAvvfQS3vGOd/i6r27oWYcTBOSg89PlsCwLnudx/vx59Pf34+zZs20fUEEckHYipigKFhYWMD8/39Z6JwCQ+urhNCuXY0Vt5DBCFfcux050xHgGoWJ7HYClSP2qVL7xQ7BHn2prW3afp10Bwvz8PBRF8aUDQjcJTicwio2W+HAWlZXG9yM25EMvPwtacTivvPIKvvKVr+DkyZM4c+YMAODTn/40Pv7xj+Nd73oXvvSlL+HAgQP4y7/8yyB22ZaeFRy/Dw6zjgB+FA9UKhV1bY2bcuGtwsrhSJKEy5cvg2EYdUKqFcJr/wNm91rlcowQZ8GV3c/EabVMWkxlbUXHLLTWDTgVIGz3DghbXSYeH+7supVyuayOSnDLG97wBsv36Tvf+Y4fu9UyPSs4fkNCX+QAbdflyLKM69evI5fL4fDhw10tNoC5wykWi7quB26QYklwLsuhvbocMZ5pcjlCvA/hivm4abv73OImf9OOy2nXWWgLEIDmDgixWMy2tYqWneJwiLsR1vTumIiN0d1wv/yfAtuXXpr2CVDBcQ0RHOPI2VZcTrlcxqVLl7B7924cPHjQz90MDKPDWVxcxO3bt3HixAlXFTDCa//D9n4lloQcdbfiXkpkPLkc0/2JO4+g1rocyaRMWkwPghHdDebzI7TmB247IARZgNAOQYueVSiNYZtfN8hQGqGVHE43QwXHJWYdo1txOUtLS5iZmcHjjz+O/v5+LCws+JrcDQricGRZVrtumzUOdYMXl0OwS9Rr72vX5Yhxb+WjteQAIqU13W0kf2OEvzOF6METnrYfdAiJFCCQ1irFYhHr6+u4du0aeJ5XxytvdSirE4T/9ovotiEklUqFCs52wO8rIbuO0W5cDhmPIAgCzp07pzqlICrKgoBhGIiiiImJCYyMjFiO4/Ybq7CaHy7HDU65HK+0IjqdCmXZFSBUKhW1sKUXRzCE//aLnh7fCXcD1KMhNKS2A2lnCBvJdYyOjmL//v26E8h2GV+9traGXC6H8fFxNSHtFrNwmtHlCJl6joHj2293Q1yONmzWTi5HTGXByM2fvRCtV+OZuZymx0a231WqtgBhdXUVZ86c6akCBCPShnlFY2RoAMJa/aJDkRWd2ASZvwFoSG1b4eeKeyvBIWG1C//iDRh75Z9195Fy4bm5OcsOz0HO2vGjlFWWZdy4cQMbGxvIZDKexQYA5EgcbK3S8j5Uhg4hzJu7HLOFoE5Y5W+swml8NINYxd7luBEddXseXE43lSP7WYDQCkGF9czcDSkY0IrNVkBDajsUp9DX+uv68I4oirh8+TJYlrXNdQQVUmtlsJsRMrtmcHAQp0+fxqVL3kvA+cv/6OnxUjTpi8sxw8nlMLA+oVXjWUfR8UIrobVuo9MFCEF0GbALpUWGvJUjB0E7rW26ke3tgTuIXUiN5G9mfu6tAOodnicmJrBr1y6cPHnSNrEeVEitXSFbXV3FhQsXcOTIERw5cqTt/ZQjzRVo0maXARJOs0OImpcf1yLmi0yLWfPqP7vqtGqsvTUWteSAZcGAGcWFGVeP6xaH44RVB4Tp6WlMTEzg2rVrbXVA8FtwvIpNeCBr+D34PE6vCU5PO5xOhNQI2dMZ5ObzmJ2dxdLSEk6fPu3qixJUSK1VwVEUBbdu3cLq6irGxsbUK9NW3kuv7oagdTl80ro6jY/bCwQf60e06l87Eq3LIfkbI5XEIOJl/YJQu/xNcWEGqdEjlvdv1+qwIDog+BleDP/TV3W/W+VvtNQeNEKm4YF+3H/mFxD06jlBEBCJRAJ+lc7R04LjJ07CcPIf/icm3/y/Qvr4L+Pcn33D9ZVYUCG1VrZrNrtGu712T35muZzy0EGEa+5CaEI0bZrLqUVSiNSKrrZhJUJ8rH61Wo1lEas2Qmd8VJ/XcRNaMxOdnY4fHRD8cjhGsTHCaF6D5G/CA1md4ADoWJHEdi/G0EIFxyUcx1mGAtbX13HlyhXEAOTm856+IN0iOE6za4IYeWBHO7kcbWjMTGDadT7VeBac3N7aKSHUCDHauZxuKhrwk1YKEGRZbvu9cBIbbmAQcq5xQWEMo9Vvq4tm0GXh29Xd2tE70hkwZiE1Mjr5+vXrePLJJ9UqtZWP/Lyn7W6l4JBBb9PT03jiiSd8a1leujYBMdScKDbL5ViFnMzCaSSXYwynWeVyrCCOxoxWczm1cOPvqCS8BVvc5nN6FVKAcPz4cZw9exYPP/wwWJbF7OwsJiYmcPnyZaysrLR1EtaJjckwP27A+TMjYjN16n/viPPotQuOnnY4fn5QRsGpVquYnJxEX18fzp49q/vyzU/Mwe1pO8gcjtPB6TS7Jmj4lH2xgBBOICyU23+dTUdjJzJGjKE13fY2hSXB27ukSmIQIbHq+jXXl+4iO6LvSdcNJ5xOX2kzDINEIoFEIqHrgLC4uIhCoYCJiQm1A0I2m21qN2VG6MI3rO/UOBWtu9FiDKd10+TR7QR9x1yidQz379/HhQsXcPjwYTzyyCO6L55XlxNkWbTddluZXeOW0rUJ9f9mLscMLwsjvVasWUEEyEqIjPmbVijFvJXWri/dbfs1/WarRY8UIIyMjGBwcBDj4+MYHh5GsVjEpUuXcP78edy8eROrq6umF2+2YrOJk7sJD/TrqtI6ITi1Wq2nCgaAHnc4fsJxnDrkqlAoYHx8HNFo1PLxbl1OULkRKyHzc3ZNq7hZCFqJW5+oK7F+RC2KBKzCYZaiYuN6ytF+WxfjdL8V2vyNGWZOZyvZasEhkJM8y7KquwHsCxAGb/4TAIApu+86DgBsf9bS7QD1VlVB53DK5TLicXcNbbcLPe1w/DxIBEHAysoKwuEwxsbGbMXGi8sJ6kA2ExxRFDE5OYn19XWcO3cuELHRuhs7zMJpZi5HCFs0wrRwM9WwuVMqR4KZ6V6O1gWrZvG6gDuXI3D67xNxOt1wsu+GfQCsXQUpQDh69CjOnj2LEydOIB6Pq2LThDZ/09/sbNh+/UWLYjiO5J/7jY44nF5rawP0uOD4xdLSEqanp5FKpfDQQw+5PvgKi50fSUswCk6xWMSrr76KgYEBnDx5MrCrMynULMRmYTW7q3w7d9MOZqLjJEREUAi8ibAYH2OG19CawEWxcv++p+cERbcIjtv9iEQi2LM27bzB/kGgYDER1sLdcH31z7oTgtNrs3AAKji2SJKEK1euYHFxEWfOnPF8ks7N5z1VrPmJVnAWFxdx6dIlPP74464HpbVCfuZ1AOaio6WccO4soEXrciqaEJjR5ZATv5XLsdwfE9GpRBp5IjeCYgYf0p8svIoOAJTK7RdNtEu3CI7bkzxz5WVwFYd1WSbOBmh2N8bfda8T8HtCHc4OolgsYmJiAslkEmfOnEEsFvNUTTb2yj+jf38GhcUc8v/hlwLcU3NYloUoirhy5QqWlpZw7tw5V4PSgsKtywm6q7KVo2k35FaKOA90A4D1+F7P297lU6l6q3SL4LjZD+bKy823GfM3FmLjBNfXD+Etv9jSc1uBOpxtRqsHycLCguoIDh48CIZh2hpPUF0Lfm6LEVEUMTMzg0QigTNnzrQ0KM0LxN044eRuSlHzK8p2cjlGMWlFXMrRfkunQ5yMW9ExYszfGH8HsKXhtW4RHCeHYyY2TYQsSqgzzd87tj8LaW3rOkaUSiUqOL2MKIq4dOkSVldXmxxBK9VkR/78mwDgyuX4Wam2srKChYUFjIyM4NChQ76eLNzuZzu5HGMoilBxqCjzipUQacNpWqqMPwd/Mex9YamohHFvZWtygttBcFyJjRFt/iavz9kYQ2kkd3Pp0iXMz89DkqTA1yf1WuNOgAqOSj6fx8TEBAYHB3Hq1KkmRxDkAefXWhxZlnHt2jXMz8/j0KFDvs+kt1pMunb7KkQ2+PUC1ZBFRwKPFWtA8KE1K9EktCI6ALZEdLpFcKz2Q5q5oPvdKn8j91mE0kzcjW57fY2LGdIBoVarqR0QFhcXUa26X+Drll6b9gn0uOC4OUgURcGdO3dw+fJlnDp1CqOjo77uA3E59y/PWbocP9rbVKtVnD9/HqFQCE8++SQikYjvC0qdFpMaMbqcUnzQNFxEXI42nOZ0wnaL3+XQJU4fNjPbT6vQWo3RXwAUw1nT98OJTotOtwiO0eFIMxeaxMaIEq5fCJmKTSbrSWyEt/wiEokE9u7di3g8ro5gEATBtxEMWnrR4ezohZ/G1i6dmNHO//5vIPorn9HdRtrbuGnRYcbq6iqmp6dx7NgxDA4Oqtv0W3DMtrl2+6r6f5GNICTXfH1NQnFTjKqhJGKivqknEYGY3Nzss8okEFOaK70qTP1AjivNzykzKSQU/VWyNpxW4vqQlKxHUgNACWkk4bzYsMj0IaU0tuVWgOaW6/t3YHfwC3e7SXDIfmiFJmTSQVz3vE2xYUsucqmZbCO8ps3ZphoXLkT4zEYwbGxsYH19XTeCYWBgAH19fZ7PL+VyWR1u1yvsWMEhHZ6PHDmCkZGRQF/ryJ9/EzM/91ZU1/KIDjRf/fo9u6adbdphzGNpxcYKKRQFJ/Ioxe0rg8yKBfhQAlGx/bJgK9ExgwhRJzGKjhFRsb4QmVsuBi463SI4iqKAZVlU566gtUszDdq/hwiMVmy0pPQu2SqXZNUBYXV1FTMzMwiFQur9ViMYtFCH0wMoioLbt2/j/v37eOKJJzzHSNs5+AqLOcQGMoDB5bQ6u+bSpUtIp9NNs2ta3aYTxhyOxIbAyaLuMW5cjsBFEZZ43W01NoaI7C4ObuZyAKDKJnUup8yaJ/+1VJika5ejhbiqEJpDJ7xcF363LgdwFh07ghadbhGcEbYMVMsIC9ZtkbT5GyE9gFDV3ZwkSzbFRviJd6s3uV0PZDaCYW1trWkEw8DAABKJRNN7XKlUek5wdlQOh+d5XLhwAYIg4OzZs57Fpp3SaJLLISXS0p9+WrddL+Kwvr6OV199FQcOHMCjjz5q+uUPokebNodz/84NAHXRcSKX9L72hMCHEmo4zQxjTsUKuwozK1dTZuxP4rzsHP4qoS56xvyNGUWmtbJqoC46s8vBLBLtBsGpzl3x9Hg7sZHShu+TWS7H5jhvtY9aJBLByMhI0wiG27dvmxYg0KKBbczq6irOnz+PgwcPWp6knWjXNaT3bHYnXtuAmGtczbodUUBm11y7ds1xdk0nQmrtoM1VFMOb/chY91V1VhVrVdb5itBKYKxub7ccmoiOEcEkVFaQnF2ZGfLmoRyE6Gyl4BTu3bYVG2P+RkgPQEg3d3RQ2LpANImNFhJOS28WCqTMC078aGtDRjCMjo7ixIkTugKE73znO3jiiSfwox/9CD/84Q+xtrbmvEEAzz33HIaHh3HixAn1tk9+8pMYHR3FmTNncObMGXzzm99sa7/bpecFR1EUXL9+Hbdu3cLY2Bh27drV8rbacTgAMPy7fwag2eW4EQdBEHDx4kWUy2WcO3fO8conyKIB4m6s0JZIF6LtTX0vsRnUFO+VXGbhtCBcTknS30/CaUaKsrMQ1jYFSCs6ZvkbUbF3lbPLZV+FZ6sEp3Dvtq/bI2LDFW2q/BzEBgimjxopQDhw4ADe9ra34Xvf+x4GBwdx584dvOMd78CP/diP4fz587bbeP/7349vfetbTbd/5CMfwcWLF3Hx4kW89a1v9XW/vdLTORxFUXDhwgVks1mMj4+3fdC0Kzha+LVNh/OnnwZ79l87zq6ZmprC4cOHsWfPHlfbD8rhlHKrABvWjVg2y+UYEdgowrI+byNwUfCsfuGnl1zOGjuMKPim2924HC+UpASSnPUJvCSlkOTazBUYKEhppDlvLfWNzCzV38cjI+2tx+q04NgJjV3+Rg55Wwsmpfr14pM2Xzyszd8A9ZBa0I074/E4GIbBb/zGb+Dw4cPI5/OOYbw3vvGNmJ2dDXS/2qWnHQ7DMDh16hSOHDniywHjx3oZo8sBgKPTf2c5u2Z+fl5dI+RWbIDgHI5bRDbStrvR0orLMWNVtm6tU5bczx4x5m+MTkf3WKV+InTjcrS0Gl4DAElpfFZEeFqlU4KztnwPa8v3dLeFRfu5SQTjOHJt/qaW8LjIVrRfQyPLckeWUGh7qWUymZYLCL7whS/g1KlTeO6557C+bj3jpxP0tOAA8HW1vd/joInLkQv5pu2S2TW5XK6l2TVBCM5gpvGFl1h9qMdN8YDA6k/SRbYPApqvSkkup8Q6L9rkTYSoJCdQsQhtAebCQm4z3leRNvdFcs7j2IkOgYiOWf7GjILovE3ZxWE8s1TFjcUabix6XycVtOCYCY0bpFAEfHKwSWy01BJZhKvN62+a3M1mblJONr5zSiINJdEs+p0aL10qldqeWfXhD38YMzMzuHjxIvbs2YMXXnjBp71rjZ4XHD/xK6SmdTmkeGDP+b9S7/djdo1VG5pWWZqf9fT4QngAYvurJXRoXU7ZhVuwE51WcBKdquTOhZk5nZpZrkaui7hWdJzyN27wKjxBCM7yygP1R4uxXL4drJyNlHLuu0eERhz7qab7OiU4PM+3fcG8e/ducBwHlmXxwQ9+EBMT7gYkBgUVHA/4EVIzouZyACh/8wXfZtd4bUNjx72785AZZ9Hz4nKKbKME2MzlrMH9zBwzl2OGVjDswmdeQmtGiqK7sEfe5eMIbpyOHbLSfKhfXxTUHzv8FByjyIQV98Knzd+UDUP6woZqNS9hNCJAcjIDdsO5O3QncjiEdl9ncXFR/f/XvvY1XQXbVtDTRQN+42dIbfh3/0wdzibmNhACwKYzGLnyd9j1pve0PU4giJCazHBglcbfLxmKBwiFcONkICJsujiyVWpK1PQqn1eiiDI8SrLehVTkGOKsfQ7DKsTGoNkhlqQEQoz9d6AoJpEKlTb3yzqRnReTyISaF51aURBTEGQOmbD9cyQTcXFCKzqP7NG7rXYEZ2FFv5jVjxOOUWyMyKy5sxbi/QhX9BVqUqofXGG9KZRmu/0O5HBaiU68+93vxssvv4wHDx5g3759+K3f+i28/PLLuHjxIhiGwaFDh/DFL34xgL11T88Ljp+hAD+r1AikeCDUv3nFXyqA++6fAk+/r63t+iU49+7Oe3p8LrwLHOzfo3UMIWwQIQERhKG/2uXlCKJsML3ZgLqoJDh3SWktRTGOVMj+eVrRMcJLjROiV9EBgLyQVEXHTf7GDAXWxwURn4bgZmFiQnXcXqq/H5xBjLk2Dj9jwYBWaKKCeVVgNT6ICN/I2ZD8jZXYAPq8jRazcBpQF5yg50sRvJy/vvrVrzbd9oEPfMDP3WkbGlLzgN+CM/y7f1ZvdQOACYchFxoHivy9/97Wtv0QnIW7d5tOTMbQmrF4wA+Ksn34yG2uhFCRY66S/kbKooeFqCb7ZOdutKzVmjsMkPyNFkFuvPd5ofMtT24u8U0/t5cqqti0i13+xmown5aqQ78+J9iNVUd3A3QuhxP0vJ2tgAqOB/wMU5HZNWyofhIpXpvR3c9USm2JTrvObuHuXc/PKXDmJwVt8UBRrh/QgtwsVGa5HF7W32aXI1mteR/CtsqbP6ci1gXEKDpVabPEWXTO8wiSezEuCt4FMS8kka85C49Z/sYPOOiPhWZ3o//dGFp1k78pRbMoRbOISNZhUYmNWIqNEO+HELf+Xggx96E09fU6kMMRRbEjpdedhgqOB/xyONrZNcmPf0G9XXU5pUYCtF2n0wpGsfHqciS0fqA4uRuClcupiuauggiI1/vscBKdqhRCoea+AKEV0QGgE51W8jfdihtXY0QbTgNj/14IsQwi5eZ1KVI8ZRlOAzqTw+nFTtHADhCcbsvhrK6u4sKFCzhy5Ii6INXO5QCA+KO/bes1vdCKswGs3Q1BRFh1NwRTl2NyG3E5bivAjJSE+km/VWGxC60VxbhjiE8rOrzB9RhDZ15ER+tc8jV3bgewz98QzAomOkUx1I8aZ/2ea/M3bkWJ5G+s3A4j1N2WFHex7qkDIbVyuYx4vPVqyW6l5wXHT9oRHEVRMDMzg5mZGYyNjamD0gBA+T9eVP/PhMNAJKpzOWy11BHRsRMbO5dTRKYpbNOKy/EqKNoTfVFoHJxWLseIVoCcxKgsxtRwWit4cTrr1eaTnjZ/Y0e+lkC+5n+HYYYJVoB4Jo5iqB/FkPuwqJ3YVOPN92nFRhtKE2PeSs47JTjU4exwWs3h1Go1XLhwAaIoYnx8vGkxF8dxqssR7usXwhGXA9SdDj/1svcdd2Dh7t2WnY1bClIKgkk5s1eX0y5uQmtenVBBaH58VWr+W72ITqHW3oI/Ijo5Ppg5OU75GyN2+Zsi7DtKGPM3JK8DADHBZC6SS7GJlNd1YkPcjfLYT9ruTydyONThbFO2OqTmZnYNy7K49q+eA1BfCFqbuWnqcgj81MsoT/+gxb9CjxehMQvFaE8W7bgcJ3djFWpyyuWUBP8O2lLNWvTMRMeMogch8So6kqL/fIJwOm5xEiCg/t1xEhsjpZD1zCCZ5VSxiVUthtkpzReM4YK79v/q69AcTsv0/DocP/EiOIqi4M6dO1haWnKcLEqcU2z3EKrLGofTPwgINTCVEpR4/cvH1SqQInFwYlUVncSxH/P8t/jhaPLoBwtnx1fQ9BgTlBDCjL6ztJXLCbP6q2JeCiPKNS8iLXoUlXYKCEq1CJKRxtV5RWzse0GIIh22Lu2tbbqeYi2GVKRqWvpshIhOLKT/u71UnmmFR1GATNS+jDno/E1BTiPCWC8GjijmFWmlUB+isn9jF8zcjRs6EVIrlUo9KTg973D8xG1rm1Zn10Q+9ClEB+pXcLWZm/U7w42raq3L0ZK/eRH5mxdN79PW8i/O31F/tB0DWqGotN7J2PNrOSTSq6J5+bFdLqcsmD+nLIRN76sInbk2E6TmQ1KQubZDbFryfBx53r1I+5G/Kchp9cdI2EZ8gLrQmDkbbTitHDF3StVYn+n/We14DY3YOIXTgM7lcHpt2idAHY4n3LS2aXd2DRMOQxE2D4ZyEUg0X3lpXY4UiiEkViGGYsjfvAiJa5xkHxkdwurcDUhM/WNm0VzS7BUFDEpKY59ksDqXIyssWKbxe07oA8fq3zOjyylsCkqEa3Y+Ti6nWKs7kqoYbnIB5L542H5Wj1eMLkdLQYgizLoIJ9ViiIW87VehFkM64n7UgJML0oqOk+vRYszfmKHt/RZi9X+nnbsxIjDOocpyJIOYaJLLMYhNrOJPa/5O5XCow9mGdCqH0+7sGuJEIh/6lHq71uUoEXdXuJzUfCLklMYBr3U27boct0guK6w6BXEwVi7H6T6gLjoVC2dV5N0VOOSr3gshCrWYqdsx5m+8QlxPno+rlW5uckB5IYmSGKsvQt38aaf5qRar0dyEciTj6Gxi1Q2d8ABALdp4DivWjxcxmoYYde/agxYc7SycXqLnBcdPrMSr3dk1Ta8TbpzI5Hn99EMSVuNqm72rxPoVb0hsvvJ1msLZCnk507S40NjPi1xZFwTr94FUrBU04bKaSWXXarX5JGBcy0KwCq25DYcZRYb8bvX8Em8tSkbRMf5tNbH+HuWrEc/CI0oMNqruihSSv/RmJH/pzQDUkS+2GL/iWvFRfzTi4jeCEkYJaVOxaSV/YyY2sUq9I7RgEBjuyJjn7QeFH7NwuhEqOG3ix+waI5EPfUonOoStdDl5OYO87L6iyCg2frscXgqrITMz7O7T4uRk2sGt0wHqwmOVv7Fioxp1LTytEvT6G6f8jRVWoeFy2Pw7Gqus65yNVmy8OJtOQR3ONiXISYV+za6xQ8xtQKWBAT4AACAASURBVJ6/DbZcL5EWMkOQIvWQhRuXExROLsdNiGeNbz7QtU4gvxk64iX3YuXkcswEpq3QmsHl8IJ+X72IzkYLIbb685pFR1ZY1dkA0P2/HTiPAuQ2f1OUkihKScNjzfNkZVb/vSH5m3I4g4TQPN3TimhptSvFBqA5HIoGWZZx5coVLC0t4dy5c8hkvK0lcIOVy9HOaneDNqymdTle8OJsAOtOxlqX42URpBkFPoKqaB7qsnI3dqE1K2Ep8RyKfPPztNuyC60BwGrJfYVZK6IjKUyT2/FLYJxoatDJelsYrRUau1EUEjiU2XST2BCMzsb4O3E3scpqUygN6K5wGlB3OFRwtil+uhxZljExMYFEIoEzZ84EOhcjNFif/2F0OQAgReLgU0MQI/ovJXE5ZmE1LW7Cak5hNDOXoxUbNy7HLGRUk0KquyF4cznew3cl3v45ZqKjf7696BSqjeeT/I2WmiacRkTH7L0RJfv31C7MlvqwvQgFGAxows8ckJPYVEON12k3lNapkQGlUomG1HY6KysrKJfLeOSRR3Do0CFfhYxhmKYvM/vsRxHeNdQYzparJzvNXA5nE05rpXjAq6sB4Kp5pCRzbbsbLVYux0x0inzIVlicRMeJ1aK9O9GKjhOthtcAYOT5N7T8XC1B5G+0QmO2iJegDacZp7jGlEbxgDGXQ8SGhNaqoSQSteYwG7dZnSaE699FLwu6gwzTE3o1pEbX4bhAlmXcuHEDxWIRmUwG6bT/cV+yxqfJMXEcsLkuRy7kIYciailnqFaCGEmikhgCAERqeiHipJpuXQ5QD6up63IUST1gyf+NHZ2dkBQWHGO9DkdSGMe4vyBzurUreb5+hR4J6U8CvMQhykko2ORFijXnIoASzyEZlXS/Wz1Ot20+hFRU7Ngi0Hw1hEzM28WCX2JjhvFzdGpfUxHDSEdE9QLDzfokI0ax0VJGCjF4WD8km7v+GSmNjR/9CKFQCIODg8hms0ilUqbC0ok1OAANqW1r2rki0c6uefLJJxEOh30fMw1YNwZln/2oLpcTmrte/1fjcsgo3lokhVJ8EHy4+Yvq5HIK6PMsNlrctsbP12IQZX+/dl5cjhPthtaKhufzhvDZAwcXZCRfDSFv44y8rr/Z+6mfbss92aHN35CQqFs3a8zflOSEKjYxtrldUBn6KsiK0ixM2lBaVXNMGN3NI488grNnz+L48eMIh8OYm5vDxMQELl++jMXFRfB84/U70UcN6N3WNtTh2LC6uorp6WkcO3ZMHSfg59RPLbbb5TgwABRBsHQ5RoqxxviDuFDQ3Vdm00jIBRSYzZnum9cdDKNA2TyBsVAgu5ibAgDrfMrWxXhxOcTdAEBN5JpczoNSDNGQ+ftk526MQmF0OW7vs6IqNN6rIs8hZfN8o3OpmZRDi7KhEWc1BFFibB3PI7/9Nrit0TKKDssAmZjzBE4rCrUYOA8FA3bhtIKYQIwz3xdZYT2JTaKW14kNH04hIa6pYhM78Jh6XywWw549e7Bnzx4oioJisYi1tTVcuXIFoiiiv78fyWSyIyG1XnU4VHBMUBQFt27dwurqKsbGxnTjBPya+mnErk8b++xHIf/FZ9XfQ3PXUT1ar6phN+fAh8UKhFAcYYmHwEURlqoQNodYFcID6nNJB2ciNu1ithrdGFZrPLbxPooy67miyQ47lxMLWX9eXvM2lVpdHFIx+313IzoAPIfMnMJsmdE+5BfMOyVnRq07Lde33RAhs/yN8aIhxLnP8bgJpxXETUdjITZGYkwjnBZnGnkdsyKYJL8OPux+ISXDMEin00in0zh48CAkSUIul8Py8jJyuRxee+01ZLNZDAwMIJ1O+y5CdB3ODoHMrpEkyXJ2TVAhNbvtsu/6NTW0JhfyiN24oN4Xqpk39VTvR/PVpDb+ru2Fpj3RsA5dg720v1+rOodWVsvNj6lpwmKFav3vN4apCFXB29fZTmxW8va5oGLV+bVWi875JLtwmZfnPPLbb3P9/OO/81bPr+kkNkZ34zVfQ8TGjpLU/Biju6kq+u9Q1RBeTlQa7sYLHMdhcHAQ+/btw65du/DYY48hFovh7t27mJiYwNTUFO7du4dq1Z+1cJ0K3XWaHeFw3F59rK+v48qVKzh69CiGh4dNH7MlIbVNmOwglJUl3W0yF3XlcggcpJamcRoxio0xbGblcrS043J4kdWF1oy5Ey0PihHEwuavU+JZJKPe7wPqouPodKocUjFJ3WcjgshAEDmk495O0PlqCLIMpOOSK7FxcjdbRUGI24bXSP6mFbHROh3ibrRiow2nuYUIQTQaxcjICEZGRqAoCkqlEtbW1jA9PQ1BENDX14eBgQH09/e3tHSiE2G7rWBHCI4T2tk1Tz75pO2kvSAdjqPgPPMc2G/9IeTV+wCA2I0LqB4dQzVez9eEJOurqxAEiNBfcXOMBElpPlE75XK8Dvba4OuiJ8oMQqy5ayLhHEFiEeb070NN5CxdjZGqwJqKi9ntJd55m1rRIeE0LcUq6xha0oqOFYVKQ3SM+RvAev1NodL8+RnDak5iw3b43FaTQ6i5mAUE6IUmzja+39phgNpwWgL1Ypoqk0BCqecuQ7Je0ITQZv7G434D5qMJGIZBKpVCKpXCgQMHIEkSNjY2sLa2htnZWbAsi2w2i8HBQVfhN7I8ohdFZ8cLjiAImJqaQjQaxblz5xxLHrcih2N4INjBXUCtfuUXu3cd2PsIapH6FVwtFEdErNi6HDNYyE3tacywExszl1OwmZIJ+ONy7NxNsers5oxOxo0QOe6bIbxXrHIIh+yFSSs6bhn7z/+b530D6mG1qx/7pul9fq+/0YbXirVoUyGIFm3+piTEEQs153PKUhxxTn9xZXQ3pvshNnI+6b2HHR9vhptZOBzHYWBgAAMD9dxprVbD+vo6FhYWUCgUEI/H1ft7cYy0HTtacFqZXeNaGDziZtYOUHc5yrf+sHGDZgy16EJYAH1Yzcrl6PYNCnIuy561bFSjYA2OxszlGLslG11OYVM0Ig4nbIIXl0NoK7RWYZGK238neAHgBQapuLPoxG1eS4sbsfEjlNZu/saukapVOM1ObIw05W2YBBJy/bjg2QRC8gZqXEwNObdDK+twIpEIdu/ejd27d0NRFJTLZaytreH69evgeV4Nv2WzWYRCIciy3JPuBtghRQPGD087u+b06dOeZ9dsVUhNheOASOMgjt27rlv0Wds8qPhQ3Y2EN0NtZsUDun2wKB7w0oLEuC5ENgkPGTELIbnlQcFiVIFFAQG53crFWN3+IG8uytVafd+LFXeHUrHS+FsF0Sx0BhTKLAplVnNb8+OcviqZ0T5bsUmN9OPsf/15F3vcOnk+qitzd0NJiKNkMjI8zlZNxaYiNS6yEiiiyjQcOM8mkBQbocV2xQZoP5nPMAySyST279+P06dPY3x8HMPDw8jn83j99dfxm7/5m/i1X/s1RCIRiKL7CsbnnnsOw8PDOHHihHrb2toannnmGRw9ehTPPPMM1tf9GUDXDjtCcLQYZ9d4rXXfyhyOoiiYm5vDD9OP6UWnVKiH1jQUo1nbbXFo/A1WK8a1bUi8xvnt2uZrBSZfNRcM0qq/oAmJ1UxO0Ha4CadpcQqllar2r9+K6NihFR0jb/xvP4vkcGvuJTXSKIn3O3+Tr4RthcYunGY1wqIkRHViQ8JpFSmGBNcIkxnFhlDjYkjyjZNtq+E0wP/x0iS/c+TIEYyNjeH555/Hww8/jJWVFYyNjeGnf/qn8eUvf9lxO+9///vxrW99S3fbiy++iKeffho3btzA008/jRdffNG3/W6VHSU4xWIRExMTbc2u2aocjiRJmJycRD6fx9mzZyFnBk0fFxXqCdTIpqvhQwkUuX7wmylSJ5dTFOLI15LI15JgHMqirViv6kN7Vi5HKzZuXY6Z6FRNkvn12823uVqw/twrfHtn4GKFbcrf8CZveTui84av/qzj87Si4gWv+ZuNSqguMps/RqKcu2OlaDLFFKiLjRlaZwMAFVnjdORGmLm2GWb2w90A/guOkeHhYbzlLW/ByZMncfHiRXz2s5/Frl27HJ/3xje+Uc0ZEb7+9a/jfe97HwDgfe97H/76r/86kH32wo7I4TAMg3v37mF2dhYnTpxoa5xAkGXRVkJWLpfx+uuvY9++fdi/f3/9xqfeAfn7fwVmY7VeQFAqIDP7I+QPPWn5GkWl3rpG0FQIkfyNm3YzLAPIDucjtyGUtVIYIQe9Xy2GbPM22gqtao1FLKIpk3ZwG9Uag1hEv20iNhWeQTyqNN0O1F1OMqao2zCjWAZSDoV8glD/cXocABTK9ddJJ5QmsUkO96G0ol/oScQmNdKP4lLO9D7C2Fd+Hv/z2f+m/m4UHM7wNhrzN8Z8nFNhhBZB4iBYdAGPhWqq2CQMuRyj2ABAkmtUqhF3kxTruRty8SVwUQzs3ut6/8yQJAnRaLBD70jjToZhcPToURw9erSl7SwvL6vpgj179mBlZcXP3WyJHeFwHjx4gJWVFV9m13Q6pHb//n289tprOH78eENsyHN+/J1AQr96OjP7oyaXE97svEumK4bZ5tiwtlJMu37Gi8vRio2xlLrVXI6Zo/ESWrMShXZwCq0BddFxg/ZxosnXSnsbEZ6dgJWz0ULCaVp3U5U1rZE0RTQC549IBO1wgN7tMgDsEMEZHBzE6dOnfZld06mQmqIomJmZwezsLMbHx9Hfbx4iUcJRoH8QSDYab6aXr7l/XYeOv0asYv4b1SjcjgrJV+qfg9kJtvEY+6+m2foTN6E1rVjYiZFTaG3VvHsMeM3FeCuiY8dbvv4ux8cYHYz2d6sw20/904cBBD9OmuRvCnykqeN3PNSIO1qV0pfEZtEwik2Srb+ZNaW+jRrTymobazohOH7Nwtm9ezcWFxcB1KcTWy1m7yQ7QnAYhvGtzLATrW0EQcBrr70GURQxNjZma+HZH39nXXTC+oNUZOu/RwyLQYNwOVYFAkG6HMGmgMdt8h5oiI6ZwFR4xlZ4ShXnE7RfovPOf/4Fy/tI8YBd3qaVnI4xnOaEMZxmzN+YCY3u/loEhVoEiXBz0stObLThNKAuNkkUUGNiSIk51d20G04DOtNyxq9O0W9/+9vx0ksvAQBeeuklvOMd72h7m+2yYwTHL4JubVMoFPDqq69i7969ePTRR11dTSns5gGwKTpMpYSRuR/qHhO2mA8PeHc5Woxi4+RyiLshmLkcJ3djJyh2LsdNKMxI2YWo2MHXFBRL+m0IJkUENUFBvlj/IZD3xk5sCHYVa3ZikxiuJ5qJy7HDKX9jRYEPo2CYiGpsqGrlahKhmio2yVBjTIDRjWlDaVr8CqUROjEPp5WQ2rvf/W78+I//OK5du4Z9+/bhS1/6Ej7+8Y/j29/+No4ePYpvf/vb+PjHPx7QHrtnRxQN+EmQDqdQKGBychKnTp1CKuW+sy1HCggE/dyQobuv4c6BNwGKXnDCjABBCSPMiroCAqDuckgBAcvIkDfHSDNQ1HYiLAOsV9wdyDIYtQnoxqbYcA4nKlFimk5uNZFpKiAQRCBs+AaXNqtkoybnryqvIBY1q3Jr/YKkVFGQjNefz9s0OS6WFKSS7l4nX1SQSXnbJ8amvjkxPIDyyprp7UGiFZmIxUgJwL5C0czZlMUIkuHGd52ITZItm7obgYlg9/BQK39CE50IqbUy7fOrX/2q6e3f+c53/Ngl39gRDsdPghAcWZYxNzeHUqmEc+fOeRIbgpjK6kJrTKXeQfrg3HfVx9Rk63CGF5eTs1ljA5i7nA2Ns5EMJxity8lvlgFb9Q4zuhu70JpbSmXF1MmQ24z3VXn971ahNb6mv93odOwgTkfrbuKD5gUvyZFBS/EIWlSMFCocChUONRe974p8qGlOkTacVjJxPWXRMMFW87015m2I2PhJpwSHFg1sY/wMqfnd2obneZw/fx6RSKTlzrIAEDn5ZkjxTaEKNx9kwubBWBTrV068VP/dSy6nwEdUsfHylubK7v6mvM1CR8C5Oq2kmTZsdBtEFIxiocUufOYUWnOTzwGsw2lmuAmltYqZEL3tH39Z/b9TOXRFs0i2UOFQFVjTQg4zYiHJcXJqqRZBItJ4s5IhXhUb4m6qGvEJM/rvsaA03JVf7gboTA6nXC63dNG5HdgRguMnDMP4Jji5XA7nz5/HQw89hIMHD6pdYlslfOZfQcwMQk6kocQblnz/ynn1/xFWUEWnIOivooxXj0B9kqPVynE70XH6U+xcTuM2/WOKZQY1kxO2lcuxCnFpRadUdv+e24kOzysolZ2/F4WSjELJ+XH/5sIHXe1TcsR8ATCgFxWr/2sJDzoXFmjb7hA344Q2nFascjqxiYWbP3g3zqZq8l0FGkUxKeR9dzdA53I4vdrUc8cIjl8ux4/tkBY109PTePLJJzE0NORbMYLChSGHIlAijXJQtlrC/pXziBjmxkdYEQUhgaoUQWGzf9UGH8cGH0dJiKKwufpbm3NxGhVtJF+un5AciwnKrG2ZtBNad9N8n3dRsRIXO4cEQBUdYzjNiBvRMUMbVjOKjRtRceKnL/97FEoM8oYfY3+3VnDVudtMbCxGhyfD9Q+9uunW+c2QsaCEVbHx090AnSuLpg6H4gvGFjXkSsavUF3k5JvV/2tFB2g4nQhr3d4m7LIVCcFOf4nYqPtjOAcTl2MXSiMup6hZ9GjmcqxO8G5cjpF2QmsALJ2OMXRmJTrP3fqY42u0QmJ4wJW78Xo+bSqHDhtyV1VOFRurbt3lWkidwQRADaeVa2EkI40PMRnmde6mKkWQDpXByxGkuBIEJYwU8hARbpr/5AeKogTeyblSqfhSFt2NUMHpIOVyGRMTE8hmszhx4oQuFuxnF2ricrSw1XoRAXE5RHQimzkcs5HArMbNeHU5buP5RlpxOYXNZLyTqzCyum4t8F4EiTd5rJvwGgCsb+j/YCI2kax1mXN8MGMZSrMTlciQu1Dae279O/39hnSLU0siQrHCuloTVa6Z53PMnI1RbMwg7ma0xeamTgQtOLRogNI2di1qAH/X90ROvhl8crAptAbo8zlWtONynOL6RpezXnD+CuYKzbeZuRwzShXFtlzZDCux0d5um8/ZFD63olMqyyiVZdfOJmoTJrISFbf3+4FWaCJh6/cpFpY8iU1ZaNzGaS6QtKG0KFMNxNl0klbKorcLO0Zw/L4qcZvgd9uixu/9Sx0da+yDQXSOPPgeAP9djldXky+Z/81al1PcTOqLUvPr1YSGuyG4Da2RYgE7J+OUr/ESXrOqRCP8n0u/7rgtwF5s7HDrbgjvW/2Mp+0XKwyKFcZ0xo/p46usTmziJsUDANRwWlkII735/4qoWd+z+d2Nbjp3IjZBuZtOQAWHosOtG/HSoiYI+OQgaslBiLEUhIz+RHUo/5rtc726HC9ioyh6sfF7Ha3qMFwWC2iFxSgy5Hcr8VnPOe+8ldMRRfv9M4bVtGITNgm5EVExiotXVxPqa4iQXTitUK6PXnA7aoHkb4pV69NOqdb8PdI6GwBIRTZHb0hh3b9RRt/GabtCy6IpOtws/mylRY3fpI6OQQpFIFu09ziUf61x0Ir1M4sXl1OscsiXuabiAD8QpYa7adxmXEgpQ3BwDlrsQmvtOZ2GoFg5rFLJ+vvi1t3Y4UVUyGOdyqCNLqdQUlAoQ/1xfJ2m4gFWFZtEtPl9shMbM3eT3qxSy4RLqCn1IgFJ4ba1uwFot+iewO/Fn3aCs7i4qLaoGRkZ8e11W0FmGgexFGnU9nO1+sF6svKKWv5sxMrlbFRCus4BXsmXmOaKNbN1OG10EVizcB58zdvaG0K1an+BoRUdI7Va/T4z0fnV6n8E1+98gvSat7FyOwQrsdG6G2BTZDZ/HPfRJnVi54LiYUkVm2Sk8R4Z+6VpxUbrbmpKGGm2oM52CgpZlgMvGADqlazh8PbOQ1mxYwTHT6wqymRZxtWrV7G0tNRyixq/mVop61yOVnQIZ+QJAHWXk+ejqAgh5KsR5KsRFKohFKohlHhOFRqty/Fq3KzyNoBedKzawBCXU9SUFFu5HJ43FwGr23Mb5gpnJTbG7diJDoGIjigq+NXqf3R8fCTbZyk24WyfaWhNfa6N6wkNNFe5GcUGAH6R+S+N+0P6zy7i4pxIcjvGYXeEUpU1dTYVQX8bEZtUpKoTm0y4Xn3JK/WLpgO7gzvmOrEGp9eh714LmK2ZIS1qotEozpw503KLmna7DZiRfPhJU9EhLocTq6roGNG2NHHbHdgKo9hY/alasTFzOcZSYkAvOnbVYXahLcDeyTi5HJ6XUC4727JSSWoSGyuXE9plXyTA2LRZ4bJZT7f7SU20djUknFayyOUYxUb7vSNiQ4oFakr4/2fvzYPkKO88729m3Vd3V19St1pHC91qdat1gA3mGGMwBkmALcAYDCxgGGNsPB6PBxl7jc2OiTnWMV7Pu+/G+t2IfWMOPBOBwBcDxmM7NjA2IEB9qHVf3a1Wdx191J33/pH9ZGVlZVZlVWcdkuoboVBXZVXlU1mZ+Xl+x/P7wUNnYzdzc3MVqeYOVAc4lbj+60kN4JQhrUtNXaJm7dq1ZZvdFEVZfsKRz0y55NkrgQ7j17+RkR4mDlvhi7ZUK8fIstF+3YW4td/frJWjhokZ6Bh9LoAc6BB3mlp/Kb1o+F49GcKordVwmxnYqK0cPesGAbmqgdrKKSaz8R0CG48re3x8TkGBjdcpH8OMCj5aFy8n2sCLdgiSDYJkg4dOIxQK4dChQxgeHsaFCxeQThcoQVGiqlHWBqjO4tJa6YppT1CJGI4kSZiYmMDU1BR27Nix5PpHJPvNypOafGbnqqsQPcfDLrCwC/LPnhPT4TPYbn8Xh+mr8z7DbpOUFf92WtItJ0/TgNHEspAbzYx4HtAajBwvwaFx8XCcpJt+zDAiXC46z7ohzxeSHnwyGaHo+ZRK8fB68y+vA75/gJgo+FZFhawbe5uxu6xUC0YXNho9Sf0P/C9ke+Zo3WksZ7w2SutOM2vZqGGT4W0KcIh1E3Cm4aEzYEUnepd7AHjQ0dEBSZKQTqcRjUZx4sQJMAyDlpYWtLW1oaWlpezim9Uo3Hm5WzhXDHCsFE3T4HkeIyMjoGkau3fvtuREtLoSNZCbwm0PLgc/Ny3/LWTAO32ws8mc128X38Vh29VgBBscNhGcYHxDttFSXhFOtcyCRpLkxaMkK00QjbtNxhOFjw/HiXA4lg7sTEaA2238m2qBwjD5YEqleNjt2bEc8P1DwX3aWpohzMu9q4u50szKFgxCmJtT/tbK3tqmn7ER0G+FoJY6kcDlLP5bJ9MUvAYdn9MMDZ87+9sS2PhduS5KlrfB6eTBiTbYRTtY5FcboCgKXq8XXq8XK1euhCAIWFhYwOzsLM6cOQO73Y62tja0trbC5/OZnoxWw6WWyWQu28KdQMOlVpZEUcSJEyd0S9QsRVaWt1F/piiKuHDhAsbGxiDQ8k2St8lXPu/MLjCz8bIvvI8eVp4jrjWjWI6Ra61Uq0abAi1ouMLz+bDhNOtYkinjYzc3rz/9ZhjR0IU2N6efR51Oy68vFq/hWBHpxdeoYUP7A4bvsbU068JG7TrTWjfqbXpQsQWDxlZPk7ErTS3J14RH3f+MRFJEIikWzFrTa36X1InnEHeaFja0tpsnb0PAxYLlbfA7GXCiDR47B68tDQH0onVjLJvNhtbWVqxbtw67d+/G5s2bYbfbce7cObz77rs4evQoQqEQOL3eESpVqxfO5QycK8bCscqlFg6HMTU1hRUrVuiWqFmKKtG+mqIonDx5EoIgYPfu3bDb7YieOw67wIK3uQ0tnZ2OD/E+N5jznNq1ZqRy3Gck46xQ10pAzlCz2zRuNF3Xmr6Vw3IinDrPp9MCPB79SUOhbYAMHZut8LiLWTZqUQXSYW0tzYZJAraWZoAq8WZIYBNsA+aipt7ylbaX8N+i9+c8V8i6EQR92AC5PXWIUgwFv1sGjt/FI8PL35dd/J8T5f95kQZLl5c67Ha70d3dje7ubqWtezQaxcTEBACgtbUVra2taGpqyrlvVCOGk0wmL9sqA8AVBJylSpIknDlzBrOzs+jt7a3IiWc1cFiWxfz8PLq6utDX16dcPEl7M3xYgF3IzuDT3nZ4UpGc9xPoZDg6r8qvOpaTylCKRWKzlVY5IFGgTL/atRYvkl2mtW7U0Emljd9LrJSlQEcQJEPofK/DfMCdDspBfCkR091OtbQB8Xn9N7e0AQtz+tuag8bbtDKwbtRyOEy4zxYtVnVLb7U7LZVBnntNho3KrbYIGT3rxr4Yx1m3fGnVO2iaRnNzM5qbZSuR4zjMzs5iamoKx44dg8/nU9xv1YjhXM6LPoGGS82UtCVqnE6n5a4vwNoYTjwex6FDh+D3+9HT05MzU1vVsxxJezOSrhbFtebg00h7ZVeOnc+mme50yCVwSFHONEsrfy+1R0pM4yKTRH03jRo2ejXV5mPmV4iynPHxTavAlNZAijzWPg8ADMMjlcp1x3CsiO+t+WfAp+8+07rVCGyMRLUU3m6o5mDu/0RaV1qwTf5nQk8s+7nhNpez+MJaLWx8bhEpJhdiGS57XqmtG060WQYbPTkcDixbtgybN2/G1VdfjTVr1oBlWYyNjeHkyZOYm5vD7OxsxVKvL+dK0UADOEWlV6LGTGmbcmRVDGd6elqpdOD1enUvjlU9cgUExuFF0t0Kzi77jVln/sK561uG8PH2w3nPq+tqqYP8ZiaBBDZaxmihs6ADEz3oaOM5gGzl6Fk3BDpm1syoNTfH5D3HMNnPUEPne2v+2fTnamFD+YsH7HNEYKSFivYxkV7cBoDoLW7dEBHoqN1pctXr7O+gtm6IUjrlzvRg43fLvxvLyycWI8iw8drZnL45lRRFUfD7/Vi9ejUGBwexevVqeL1eRCIRHDp0CENDQ5icizNUbgAAIABJREFUnEQqZSIP3KQaLrXLROXEcC5evIizZ8+iv78/p2pAJYGzlJmTJEk4deqU0tzN4XAU/MwFsRnN9ALsIgvW7oGTl9cssE4/nGwCvD3X5/Hx9sP4TWS7qVhOIWktm2ISBQm0gcuqUKIAAHCsAIczn4BGlo6eBVOKUikOL677ienXF7NsAI11E2jJdauVYvkQAOmk3pqFjeDJWmZPLPs5/vuFPaZ3rwubDOBbjJH73aLGsqERcHFgBBuaXLI7zWWToV4J66aYJElCIBBAT08PACip16dOnUImk0FzczNaW1sRDAbLXvjdsHCuQBUrUVOJ4D6wNJcaz/P48MMPIUkSduzYodRiKjTWzaua5M6ItJxWxNqz2TFJT/ZGZlPFerSWTqlWjh5sjKycRMLYAjFj5RSyYNIp44ykTMb4fYW2AdCHjYFbjVrZW/CzgCKuNL1tRi40oiKwEZuM96eGDdGTvb9R/jZKHkhncvdJ3GkybFSVuhdh43cLOZYNILvTgi45sWV9l37jtUpLG8PxeDzo6elBf38/du3ahc7OTsRiMRw+fBgffPABzp8/j3g8XtLamsu5UjRwBVk4ZsUwDIaGhtDe3o5NmzbpWkb1ZuEkk0kMDQ2ht7cXXV1dJX3mqp7lGJ+cBmjkWDoOgQHj8MHFJfPeQywdZTGoTb9TpzqBIJEU88BSSFrY6Fk5Cwsc7JqsM92sNQMrh+MEOByaxYaLQMlkeLjd+pcH2aZ2p32/bzGuYbJCvhQsUrLG3wTYDbKwAi2F/ZYGsBH9siuNjhdOIBCb2kAJxTvcCU7jmbjbReWBRi2ttZNhKfgX4UNgQ6wbj4NHiysFCRRoqjKxEzMqlBZN0zSCwSCCi+nnDMNgdnYW4+PjSCQSCAQCSvab02kMzMs9Lbph4ahktkRNPcVwwuEwDh8+jL6+vjzYAObK5SRF+cZBLJ2EK3vDSrjlGa/ayhFoO27sHNX9LL0Fm4Uy0YjUMIonBMOqBcqYC1g/QL51w7GqhACVdcNxhcrY8Lp/ax8rsDEpNWwkg3iN2FxekgCBiunX67jSBL3nNNaNGjZqK4dIDRuPOzdTjcCGWDc5sOGyr2UEGzieQotLjpFQkGriSiMqZR2Oy+VCV1cXtm7diquvvho9PT1Ip9MYHR3FoUOHcObMGczPz+dNBi/n5mvAFWThFIrhlFqiplIutVI+V5IknD17FtFoFLt37zacNZn5zM2rmnByQoCd4mEHC6eQAafqoZNwt8Gfya7TsIk8BNqOm7tGAAD/cXFbjpWTTEnweSnEErmgo6l895laopRbXFMUcxeT6lk5PCfqWjl6KsXSITKydJhF4Pxg97/nPC+5faAy+VYhfAEgGS9q2QBZ2Ii+JtDJ/BRpsp1O6KdIi/6WvG1qEImBIOj4nC5siPhAG+xx+TfXc6Vp9ejGdwAAPx6TSyN53DrrnTISAE2CAJt9zHIU/B75XHXa5f9XtSwo22vlSiMqdx0ORVFoampCU1MTent7wXEc5ubmMD09jePHj8Pr9aKtrQ0cxyGdTqOtrcyMRABr1qxBIBCAzWaD3W7HoUPFW8pXU1cMcAD92b4gCDhy5EhJJWoqZeHYbLaiq50Becyjo6NwOBzYuXNnwYvALMTWrwzi5MQcknQTHJRszbj4FBxCBpzNjYS7DR4urvvem7tG8B8XtwGAAhktbJTxFIFOMYmClBfY10InmZDH79SBi1HshuMECDpxIUA/bvO31/8f2PTAUkClwKac7UbWjd7zYiCou2BKz7rJe43GlcapqlU80j+Cfz0xkPcePfcagY3fk7uN4Sg47UCXPwvbWrrSiKxah+NwONDZ2YnOzk65sG4qhYsXL+KLX/wiZmZmsHXrVixfvhw33HBDWe613/72t2hvt6Y0ktW6ol1qqVQK7777bsklamoZw0mn03j33XfR1taGLVu2FJ1xlWI18ZINvGQHJ8kzScaee2NJO7IzXZuYexO+qfsoUqqbitq1VqyCAFEiwedNCLRDL+ZKU4tldVKidZ4rJkYDnP+yW3YhCW7zrg+huR2igaVA3Gp6MBFVmWLa7TlWiwYq5LERhHhPcVcaH2gr6EoDcmFDdN+GIeVvjzsby1G71rSXGrFuGI7Cxo5ZdPuzlg0FCXTqgu73qKYqUdqGoij4fD6sW7cOb775Jvbu3YtrrrkGb7zxBq6//nq89tprlu6v1rqiLBy1IpEIjh8/jq1bt6KlpTS/dyVqnpHPLQSH2dlZHD16tKQxlwKczaua8OHZDFoccXCSEw6KBWP3wsWnwC0uEI07WhHgZnXfv2/9MQDAwaObCo9JY+UUykYDSnOtEetGT2SdDMsKedZPZnGbw5V7SRDYMBkeLrddgU0had1qQnP9WDZAFja8Pwh7wjiBgHP5ARfgTOr/3oV034YhcDaX7rmQYWSXKyBbNyRuw3AUNndGIEq5N/Vm2zxSddD4rBq11BiGwQ033IAbb7wRQOnVoymKwq233gqKovDkk0/iiSeeqMQwy9YVBxx1iZpdu3bB5So9CFmpk84IDpIkYXx8HNPT09i5cyfcboOSuwafacZNRzTY68bJiTTsFJ8DHVpaLOIJriB0AODTm4/h4NFNsNHZIpwUTelWEtCDjVE/ELV1owed+AKT95weXAo9zzF8HnQA4K9vfg80W3pvFTOw4QOLiRkp/ZI25cAGADhPMxzpBcPtahVypbG+VjiTs0WtG06VVk9igJ/efAyczYWfj8op4GrYALJlM7hiBoIGMtJirGdDlwPT0/XRabMatdS0SQOlrh/8/e9/j+7uboRCIdxyyy3YtGkTbrjhBquHWbauKODwPI+hoSH4fL6isY9aSM9VJ4oixsbGIEkSdu3aVbIPmabpkmdJ61cGMXIuBb89iaTgh8+WAAM3XKqcXwIdUn3aJvEQqOzpdNeWkwCAV8fW60KHpoBY3Niy0UInHudAl1mAlWUF8Hw+yAl0MtqyNCro/PXN7xX8bMHt043lSG4fRFe+/130BECns7EwAhsjke32tD6MjKDCeZp1t2tdabw/CErU6aDqyl0LkmhZCU/KuMCnGjZ62tt3FryUTfPmJfn4ihqvvijRCmzirAcAXzcNyapRS22pCz+7u7sBAJ2dnbj77rvx7rvv1hVw6uuOW2EdOXIkp0RNvUlr4WQyGbz33nsIBAJlt0GgKKqsjDpeopHg5ZlWUpBvPglJ9ufbId+g4w7jJmBEd205ic/0ncx5Lp4QEE8Ub2JGlEzK+xO18R1VkJ8kA4gGgf9SxTE8vnfdH8p/f5N5y4bITMA+Zx8e/W6fRs/rxW0YVxMyntx1O1rYEKW92fHqxW6UbaoMR/XfxaR2pcUYD3aulick1XBlmVG12hOUu/AzmUwiHo8rf//qV79CX1+flcNbsq4oC2dgYKCuO+qpgTM/P48jR45g06ZNS0qTLDeFe7DXjQ/PZgDRASe9GN+gOCSkAPxUdoaesjVBgA0BYS7HyqElASKVBeRn+k5CpGz4pz+uNj0GOYOnSHxHkHIWYJLn1K61TFrerk2fBoDYfCbPtfbCrSM5BUyVz3V6dN1qaivHDGhETwCivXiKrxpIvKcpx8pRQ0VtxejBhvM0g0L55z3ryMIl7W3LOzZ6rjStClk3aneaBAoxxoNda1Tu0ypYFmZUDeAspVr0zMwM7r77bgCyN+dzn/scbrvtNiuHt2RdUcAxswiyllI3SxsfH8fg4OCS6yotZc3QYK8bI+fkRXes6ISTlgPyBDo8sjeRuC2IgFC8BP6DHzkPAPj/f78KQOHfhFg2aktIlKQ815ogiLBpVpwS6BDYAPprdoCsa+2FW0eyr7W7daFTSFrYCC4fbEy+u43xtcHB6KeYK/sv4GozsmBKFePKWjzEyrGJue5FNWyIku5W+DJyDK+QK00PPgQ2RAQ2xJUWYzzQGr6SJDUsHBNau3YthoaGir+whrrigGPlZ1l9AtI0jYWFBUiSpDRLs+Izl7JIdYH1oNkJOGlOgQ4nOZCQAnBT8g3ZBgECbIjbgvCK2Rup1spR6+HrxgHI4NGDDoGNntTQSaWMs9L0pIZOJsXh+3edlr8Dn18JWnffBlaOGcsGkGFTSIK3CZJNv6QN72lS4ht5+y8AIcYtJxa4M9kJgRo2ynMOH7yMQb8d8prFVPmku1Up9qqMwcCVprZuiNSxG+JKizEyvIgrTdleJy41wNp7iJ5YllXqIF6OuqKAY6VIoU2rLgSWZTEyIs+wBwYGLDuxlwqcj22g8IeTbvgdWehQiy2AM5IbnGhHwJZQXp+iAxAkGwJS4RsXEQEPAPzvt+QOqlrYGAWN1bDRs3ISMQZ2nQoC37ztDOxicVCZsXIYfxY0DjbfmlFbOWrYcK6ArpXDeIJwsom85wEg4w7CldE/rgQq2u3kefJ+NXRyXrdoyaRcLQp0tNaNdl1WwhGEn5M/b6mutAVG/my1K41IFMW6SBqohiiKqhu4VkIN4JQpshbHCiskHo9jeHgYa9euxcTEhKUXVzlZalp9dD2NP5x0w0E7lPLwLlv2hh0X/AjYEhCQvbnHqZY86BSyeADgkY9N5Dz+f95YrvythU4yweQtKNWDDs8JsDts+M97zxX8joLdZdrKIVLDpuBnu3x5rR50P2/RrUXaQ6iVcS8WhXS3FIRKsecz7iAoqfAaspSrBXaxcCo9S8nfJ+GQx+USsz1hzLjSiOYZv1LAWg82QP241Cqtenb3W6UrCjhW3sitqjYwPT2NM2fOYGBgAF6vF+fPn7dgdFmVm6Wm1frgLE7OyVlpLhuHOOdFwJG9ycQFP7w22cViowQIkg1xSr7h+VA4XmGkL31yOu+5//6rLqSTMuwkUcqDztfumMqLQ2irIixViZaVcPA6bjWnT9fKSXta4eDym3SprRzGY9BOAFnY6EkLFQIkIwilnYE8txmjE6fJ24/dOJbISQ5wlOzSc9FZi7CQK22O8edkpcUZJwD936meXGrV0OVszV1RwLFSSwWOJEk4efIk4vG40ixNkiTLi4Ja0dTt/PnzCIVCSPiWIegWwAiOHOhwonwaxXk/AvZ8d1AczQhAzqIqZuUU05duncp5TBeZrQNydetyoaN2q6W8pdWnSnuKp41zrgBEOv8y1LNyiIpBpRBsgFy3mR5sGLsXDAAfu6A8zhkblbXWOA1U4oK8D17MfidOlH9vAhhB1bFTkoCFjBM3bzLumlkv63AqLUmSLnsr58qZNlispdzIOY7DBx98AAA5zdIqcVEtZZyiKOLIkSOIx+PYtWsXPrGFV24ejCCPOc5lb0Y2SkCc9yt/K2OAiDiaEYc12VU5YywTXqQVg1qC3SAOYXfnwabYQkczsAGAtAEcABk6RtaNEVQAIOXMTwggsCkmNVySzuaCsNGK1bFoyPlCRGAjSrQp2AD1YeFUAwQcxxXslXM5qAGcMlWuhZNIJPDee+9hxYoV2LBhQ8VnbuUCh2VZvP/++/D5fOjr61NccztX84izi8U9eXkWmxGciHPZG3Cc9yvg0SqOZiSl8jsaGmVpqSXQ1mX5JD1tOd1Pi4lz+nRhwzk0hVDdLQVhA8iWiOE2HagUel7vs7XWjZ7bLAljUKmtGzVs1NYNkdp9Rv5eyDhx/driySX1AJxqjCGZTF7W7aWBK8ylVusYTjgcxokTJ9Df349AwNyMc6kqBziJRALDw8NYv349Ojo6IEkSBEFQgrc3bODxf0444bIJiDEuNLkYOGgBcc6DgCMNQZJntSnBo8R1aIg5qbAJUf7+frq8+I5aImUr6lrTc6vxtDMvW41YORlH6VBMLjauc/GFZ+xa0DBOP1wa99lSYZNyNsHLygtF9aybDOUFbIBPMK61xoiyNUOg46BUjet0rBnAvCttPu0ETQGjo6MQRRGtra1oa2tDU1NT3nVaDy61atVRawCnIV2VAhyzzdIqoVKBo4WiGjYURSkXvgwdew50ACDOeeC1Z2/iMU6eRTc59HvHEPCIoNBE69cL00oCtaSV80aKu2RLxiGay1bj7B4leSCp6pJKKmznvd7hBW8r/turYZNx+OBWtfk2gooehFLOJt3jlKFUbjNbM3zCQp51Q2CjPJacYCQn/HT+71jIlaaFzXzarVQK/5ONKQA7lIZkFy5cwLFjx+D3+9HW1qa0Y64XC6caddQu526fQAM4ZcvsjZzneYyOjsLlctWkYKjZtGh1cgCBoiAIyhoIvXHzovycGjqcaEOKdyrQsdMieJFGjPOhyZFUrByKkiBJubPWmJi9aZqFj5EE2pGXraZn5RDIqMXRrjzocDYXHEI+iNSgKaaEKwg3rw9eYuWUatkUcqGlKR+8kia9msqfQc9SnfAh+zo92BAlRB8YwYEmu/w9irnSiBYyLkgSpcDmpvVxiKJ8XmkbkiUSCUSjUWVdGsdxSCaTcLvdNbN0qlVloGHhXEaqtkstlUphaGgIq1atwooVK0x/tpUuBDPlfEhFagDYtWsXKIrKgY3RWD6+icVrI25gMdYeY1zwOOQb+gLjQbMrN3U4xvkgSjSanPk3XRoSRFV8Rg0foDiAzLjVAP2Co6QYaSlKOLJgcIr5i0O1Vk5iEUwZu08XOklbMwSdtgiAbOUYJUekKR88kk4qNrW4kJPy50EnZ5xiae05SLJIjPcpgPE7UoautIWMK8eVBgB/siEBYbGEuCAIyoSGpmlQFIVAIIBAIIA1a9YoCTbT09M4ffo0AoGAYv1Uc0V+I4Zjja4o4FipYu2go9Eojh07VnKDN2KRVGsmx7IshoaG0NHRgdWr5cKaoigqPuti47h9WwavjbjhtElw2gWkOTs8Dh4Om4CFxVIlza60Yg3RlIgYu+hmcybzrBwjaQEEADZN22EaGouTzm9NbEP5qezEylHDppgSJiygpE3O3svQPrjFfHik6ADcknFcSAsdAhvl/ZQcj8o7PuoxLFYEt1O5FqDauiGw0SrBecEJ8u9LYMML8u9KYEOsm1u3MgAccDgcynlG/icTOHLeEevH4XBg06ZNsNlsiMfjiEajmJycBAC0tbWhra0Nfr+/oteMIAgVd6ml0+mGS60hfdlsNjBMvotlKc3SgGwFg2q43oolB5i9gAl0GN6OgJtHLONEk5uFwyaAE2xYYDzwOfKPVYz1QQKlxHe0Vk6pEkEXvKkCgABbHnR4OPKsHD23WoJuhoPOL4nD0m5dK8cINmorh8DGSClajnFlKG8edLRgKaS04IbPlvt+rXWTEVwAXPAvusvUsNEqx6LRwIZIC5t4Onc7sWoAeZJDzj/iqibWj9rSbmpqQlNTE3p7e8GyLGZnZzE+Po5EIoGmpia0tbUhGAxabv00XGrWqAGcMqXXZpqsW6EoCrt37y7rBF3qQk2zCofDOHnyJPr7++H3+w2TA8zq9m0Z/HrMhXgmFzpESc6lQIemRCWYTEEqmlhgJEGi86ycSihBq1oBwAkHCtdhS9KL1pgEOCn9BISM3QdBp9yL2sohsFG2qaCjhU0h+KSF/EmPPmxkJXgfHLZcAKutGz3YqEWsG0CGzUJKBs1ndhlbaeRaIVYEsXqSySQ4jlMsIJvNplg/TqcTy5cvx/LlyyFJEmKxGKLRKMbHx0HTtJL5ZoX1Uy2XWsPCuYxUyRhOJpPB0NAQurq6sHLlyrL3RYqCVkrq5IBdu3aZSg4wq9mEDa1+AfGMHW6HiFhGniF7HPJxirPyjS/g1C+IScDjdxROKy5FokTnudXMWDly9lwADtpcfIdYOQpsiigl+uAyghHty+uEqWyjvIZrkdRp6ERq2CQFefZsp0zEulgPAk75s8zAxsiVZgY2eqJpGslkEkePHkV/f3/OeQrox36am5vR3NyMtWvXgmVZRKNRnD9/HslkUrF+Wltby6p/2LBwrNEVBRwrpQYDaZa2efNmtLaaW2FuJD3LySqVmxxgVvdencK/veuFzy0iw9FwO+TjQ6wempIgShTirBuCSCmp1BSknJtojM1edE3OwjcqrZVjxq1mJJKiXd57/XDpVC9gJVeOlZMSi89gk6IXHlofyknBmwcVQIaNVnqWTUZwwm9Pa57TWjuLpYpYD1jBDr/BBIFIDzbxtA2CKD8uFTaAfE0dO3ZMqTEI5Fs/xCrneV7ZrrZ+urq60NXVBVEUldgPsX5I7Mfn85k676sRw0mlUujq6qroPmqtKw44VjVhI2CYnJzExMQEduzYAY+ncLkTs59bCQuHZVkcPnwYnZ2dOckBVsGG6N6rUzj4vgcuh6RAx26TFOgQ2WgpZ/2OWjQFJX1WDR+gOID0pGflEMWF7AJPB5Vfb40THXlWjtatlhDlz2BEJ1w6MR4iLWwYyZVn5SRF4xkusVDyPlcFGz0rR6sE71GgYwSbnNcvWqYsTytuUr24TSxjBzl1lwKbaDSKU6dOYfv27boxULOxH/I6mqZzrB+GYTA7O4tz584hmUyiublZif0YWT/13u3zUtEVBxyrRFEU5ubmIAgCrr76astmP5VwqQmCgPfeew8bNmzISw6wEjZEn96ZVqATT9sQ8Cy61DLy6eZzyY8JdACgycWYKlujBRAA2KjsBKLJmcyxcoibTv0a5X10riXJSXZd6OiJgxOMaG4BLyu5DMvzE2lBkxbdOVaOGjZqqOhZNinBo7/gU1Ctp+E9sGsgrIUNq3rM8otN0jJOsCpXGr8IFnXcZimwmZmZwfnz5zE4OGhqgbRR7Eed+SZJUo7143K5cqwfEvs5f/48bDabYv14vV7l2qiWS60Rw2koTyzLKskBVjZLA6y3cEKhENLpND7ykY+gqamp4rAh0oMOuSktpO1o9uTe2GOMvF6jxV1aTxpAduEQoJCU67y4jeo1S1WCl/ehF9/RWjnktW6b/vdiJBd4qfBkRc+y0QMNUZqXIe61Z4Glho38GjkuE1hM5DADG/l5Y9iI4tJgMzU1hampKQwODpadZVbM+uF5PsfyoWkaLS0tytIFhmEQjUZx5swZpNNpxfrheb7kjNNS1UiLvgy1VJdaLBbDyMgI1q5di8nJSctv2FbFcCRJwrlz5xCJRBAIBOD1ei1LDjCrT+9M41/f8cLvERFP28ALFAIeAXZaUqBjoyXlJmWjJMxn5Jtli5tR3GrlqJAbjUgQbaasHE50mLZm1CKwAWTXlR50EpwHbru+Gy4tunOKXuZs413w2PM/j8AGAFK8G157xhA2ABDn5Nc7VMeB1XGryc8Xhg0AxEpLNFQ0Pj6OaDSKwcFBy7wFZqwf8jq19dPd3Y3u7m6IooiFhQVEo1FMT0/D6XSC4zi0trbmWD9WqZE00FCOLl68iLNnzyq+ZaubpQHWWDgkPZumaezcuRPvv/8+eJ5X3ArVLA9y3zUp/Os7XrAcEPDmutgW0osr1V35gJ3PuJROkM0mrB4zFkw5Vg5pv+C0mYvvAECUaVE6o6qlhU5iscJ2hnfmQSepqr6tBQuBihY6atgoY0n74XMWTuNmOBsY2OB36awx4nXSng1gMxeXH/+nG81bN6TOYCKRwMDAQEUnQmasH7XrjaZpBINBBINBUBQFr9cLURRx+vRpZDKZnNiPFZBspEU3BCDbLC2RSODqq6+G3W6vSLM0YOkxHJIcsGzZMqxatQqAfKFduHABy5cvr7hbQE8EOvEUlQMdcuNKMHJGU7OHh42SlJRaiiINurI3UjPwISrXypllAjkzfkCe9etBR6sEV3yGmuAKJ5ckC2zXQoVARw82aU6+vJOsU4GO2roBZNgo42KcYHhaSe7Qc6WR34xIFIFYksJipZqSYXPy5EnwPI9t27ZVdSJUyPohf5PXkcWnbrcbwWAQK1asgCiKmJ+fx+zsLM6ePQuHw5ET+ylHDZdaQ+A4DsPDw2hqasLg4KByUVTq4liKSy0ej2N4eBgbN25Ee3u7MoPbsGEDQqGQUgq+vb0dHR0dFS8HopYaOh5XdtW5x5UFgmLxuLPfn0BHeU0m98aqBlA5Vk6MdcNOlw94TpRv4NqyL6QrqlaRdBPcdh3rZ9HK0YNNIagAshXjdeR+JoENUZJ1gqZzj40aNgDALAImnrErfwMAx1OKVQoA8RQNfvGhIECBzXVdhzE7246WlpailookSTh69ChsNhs2b95c8/YDWutH/Q+AUsaKJA+QhaVkGUQ6ncbs7CxOnTqFTCaDlpYWtLW1oaWlxbT100gauAxVyolNSr+sXbsWy5cvr+CosirXpRYKhXDq1CkMDAzkVQ7weDxYs2aNUgwxEong7NmzSCaTCAaD6OjoQDAYrHhc5+7Befzruy1IM4Bn8d4ZT9EIeMWcWE4iY4MoAk3e4uAlWW5EtE52lvZGa9c85kU6DzqcaDNl5cRYN1y24uNMsMWLZEZSAaX4qVZ6UAGAFJcfXNfCRv2czyV/hhFstH9zvPybyDE4+TktbGJxAU9/KoXZ2SBmZmZw/Phx+Hw+tLe3o62tDS5X7ncXRRGjo6Pw+/3o7e2tOWy00sInFAop8RV17IeAhKZpeDwerFixIsf6IckHTqdTsX4KLZ1oAOcKFrmBb9u2rWrN0gD55C1UFFQrdXKAmcoBDocjJyV0bm5O6YHj9XrR0dGB9vZ2y3v2JJNJjIyMYHb+RjidNADZ0rHbZOgAgNedC4LY4ir1Jq8AozwPSZKtICIRlC501OJFKg86pSrGZl2TjGDThQ6xcrSwyfCOPCunEJD0oKJ9nvytlw6tBlCSceTBtRhsABSEzTN7GAA2dHR0KGn3yWQS4XAYIyMjEEURbW1taG9vh8/nw8jICNra2hSXbz0rFAop6+xIwVG1241ke6oTD/Ssn2g0ihMnToBhGASDQcX6UV+fmUymJi7vaqoBHI0kScKZM2cwOzur3MCrKaOioHrSJgeUWjlAveJafZMYGhoCAOUGstSMnNnZWZw4cQJ9fX34iJ/BD3/hQgI0uMXJfJOPAi8AqQylQIemVZlPi+BRu3VKkdx3pRjsDn45AAAgAElEQVSEils5sjXlgtNubhxxxgnOXthq1IKGVNsm0kKFWDl6EEoyNvhduRaS1trJcBQA+Xj6XUIOYNQqDTa5oigKfr9fsWA4jlNW+YfDYQQCAbhcLnAcV9UWA6VqamoKFy9exODgoLIgVC/xQA0hnudBURRsNpvyOo/Hg56eHvT09EAQBMzPzyMSieDUqVNwu90QBEGxbMr1Mrz++ut45plnIAgCHn/8cTz77LMWHAHrRZWYImx9m8UqS10KQyt1s7SNGzcW/fHffvttfPSjH7XUJRAKhbCwsID169cXfB3DMDh8+DCWL1+O1atX55z4VmSiMQyDSCSCcDiMTCajuN7M+OfVunDhAqamptDf35/jWvnhL1xwOmm4FnnudasXDsoZbYU8i1r4aL+u1srRA47WytGL5ei5p4yAo7Zy4kx2ouK2G5xvovFxNLMIVq0kk3WREejowyYrhpP3T2JmetaNHmwW4iJEUdKFjZFIMsuqVavg8XgQiUQQjUZB0zTa29sV66de3GsXLlzAzMwMBgYGTMdgtJYPkdr60SqVSuHXv/41fvSjH+H06dN46KGHcMcdd+BjH/uY6ckuidO++eab6Onpwe7du/HSSy9hy5Yt5r7s0mX6R2sAZ1HlNEv74x//iN27d1taY4lciBs3bjR8jVFyQKUWcwqCgNnZWUQiEczPz8Pv96OjowNtbW2GM1RJknDq1CmkUin09fUZHqP/91ceBTo8DzT5sxlPAOBzmzvltPGecmI5AJBi8wHjsOWDyAg6LJ//PbXASbAO1bb8z0kwdqUag1YELOrtatgQ2TT3NiPYZB/L//s9Uh5s5mLycRIFCYKIkmFDCtuuW7cObW25HVbJxCYSiSCVSqGlpQXt7e1obW2teO0yI01MTCASiaC/v7/sMaitH3USkNrtppYkSbj++uvx4osv4rXXXsORI0fwm9/8xtS1/Ic//AHPP/883njjDQDAiy++CAA4cOBAWWMvQ6ZvOA2XGrLN0vr6+tDcXLg/iVqkYrSVF0axpIFCyQGVWmNjs+X65+PxOMLhMMbHx2Gz2ZSsN5IOKggCjhw5Ao/Hg/7+/oJj+uKtaQU6djsQS0g50ElmKAgC0OQrDB7idlNLu1ubnpWjeZvZ2A7L23KgE8/IEHHZ83+7DG9XoKOGjZ4SzGIqM2MrCBWyXQ82aTZ7M/O788djBBsAmIvJB43lco+DKMiP4wke37zXXPkfQJ7IDQ8PY9OmTbqNCF0uV16wPRKJ4PTp03C5XIr1Y0WdQjM6f/485ubmlrwmSJ12babZHAHR7bffjttvv72kfV24cAErV65UHvf09OCdd94pe+yV1BUNHFKqf2ZmBrt27crLpimmStQ9M/pMskAuGo1i9+7dcDgcVa8cACCnCdZVV12FTCaDSCSC48ePg2EYtLS0YG5uDj09PTkXQSER6LCsCI+bRiwh39x8XlUF6aT8dzHwFJIgUrrQUUsvoYATaF0rh0BGLYandaETSbqU6tlqZXgb3HZBAY1ahaACAKGYAz5X7meqYQMAiQwNuy37fQrBhuSqqGEjiFnYzMdKg00ikcDIyAi2bt2KpqbibRu0wfZUKoVIJIKjR4+CZVm0traivd1c2nU5Onv2LOLxOPr7+y3/fKPYDwEPwzBIpwsXXTWSnpeqXlyTWl1xwCE/BJmF0zS9pGZpVrcSMGrsNjo6CrvdXlZyQCXldruVgOjCwgKGh4fh8/kwOTmJWCympMYW60HyxVvT+OEvXEhnZOgAWWvHZpNjB0AWPEBx+Ggz2PTEC/lWTjHFM9k3OO3FAZgwAAZRJOHUhRGgDxUASDK08j/ZroVNhiVfXv7fofkJzMImnhAgiFJJsFlYWFB62ZSb6uv1erFq1SqsWrVKceuaSbsuVSRRKJ1Oo6+vr+KTN631w/M8vvSlL2HdunVlfV5PTw8mJiaUx5OTk+ju7rZkrFbrigMOIPuUDx8+jO7u7iWlZmqbsFkhrUuNJAd0dXVh1apVlicHWKVoNIqTJ09icHBQcfXFYjGEw2GcO3cODodDccsZpX4+s4fB9/9NPiVFEfB5s9ZOk5+C9lCbgY8WOuVYObE0DYA2BRcgG3znhNzfRt0jiCiRMYYRgUqx55MMDVpzGmRhszgmVv4HAH6vPmzUEkRgYYFf/Ls02JCsxIGBActcYVq3rlHadVNTU0nXBIk1siyLrVu3Vv164nkeTz31FK666iq88MILZX3G7t27cfLkSZw9exYrVqzAT37yE/zLv/yLxSO1Rldc0kAsFsOhQ4csaZY2NjaGrq4uBIP6vevLUSaTwdjYGHbs2KEUCt20aZOSulyNSs+lanJyEhcvXszLRFMrnU4jHA4jHA6D53m0tbWho6ND9wbx/X+zw+e1KdAh8RxJlOD3mZ99EgiVEsuJpWjVc/mv04OO9jlSRcHt1Lda3A5RFzQERnqgIVaM3rY0I39BkmChB5vcx9nxqi0anpeU/4VFN9pf7je/JgyQW5efPXsWAwMDS7Y8zIqkXUciEcTjcTQ1NSmJB4XSriVJwokTJyCKIjZt2lQT2Hzxi19Eb28vXnjhhSXt/7XXXsNXv/pVCIKARx99FM8995yFIy2qRpaakXieRzKZtGSB1bFjx5RsLavEsiyGh4excuVKnD59GgMDA/D5fHUJGzI7TKfT2Lp1q+nkCZ7nEY1GEQ6HEY/H0dzcjI6OjpzMpO//mx0et/y3IEjw+eS/pcUS0qWAB9CBjjZZQGfoZoED5MdGAH3gJNI03E7jy0gwCAmmGQoel86iTib3i2mz08zAhoCG/C0IEiRJwrP3mLdqALm47eTkJLZv316z9TVqy3p2dtYw7VqSJBw7dgw0TWPDhg01gc2TTz6JdevW4Xvf+15dXM9LUAM4RpIkCSxbuHquWZ08eRLNzc3o7Oy05PMAebb29ttvw+fzYWBgICc5ACh/YZjVEgQBo6Oj8Hq9WLduXdkXDCkBT24QbrdbyXr7Ly854XLZ4fPZlRm3z2dToAPInUGb/MWPid7wrIBOIi3vWxsfIVJDh7xWfj7/c5MZSnebGioEOlrQAECGyb7P56HKhk0iweKFR0r7PScnJ5V1K8XiddWUUdr1zMwMXC7Xks7dckVgs379enz3u9+91GEDNIBjLCuBc+bMGXg8Hsv6kJObeDQaxU033aRUqa23eA3DMBgeHkZ3d7fpNUtmRXzzkUgEoiji52O786Dj9WRv3NqeOYXgU8zKAXTSpHWAw3L6v4MRdHiDMB8BCwGN3jY9sOhJDRsAYBiS6ScfDzOwicVYSJJUMmzOnTuH+fl5bNu2rWZrZ8xIFEUlvsRxnOJ6q2baNc/zeOKJJ7Bx40Y8//zzdXNNL1GNdTjVkJXdOdXJAclksm5hk0gkMDo6ivXr11vqSiTy+Xzw+XxKodGVK6cRDofxsyODAAC324ZUWoQgSAj4baCpXOjEErm/B01l3W95CQSCPnTUmo8Ddlv+sXfqeIw4Phc6ycUsV5fBgvHoAuB26f+u0XnA68nflkpnvyzZbgQbAEimxBzYOByLizp5CckkD56Xjxdxo5UCG0mSlN4wlUglroSmpqbQ1dWF3t7eqqdd8zyPL3zhC9i8eTO+853v1M01XU1dcRYOANO1yoppYmICkiQtuQihNjng7bffxtVXX11X8Rogm4nW19cHv99f1X2Loojn/pcEn98JQRDh8zkUiweAEuPRSpu9RWme0MY8AHkBat5zJqHDGsTYtdBJLoJDDzjJVD5UgFzYEGnvi2rYqEEDACxLGo3l/i8IEr73sP64jSRJEo4fPw4A2LhxY92co0YSRRHDw8MIBoNYvXp13nZtNQ2Sdm1VIVuO4/CFL3wBfX19+Pa3v133x6tENVxqhWQVcKampsAwDHp7e8v+jJmZmbzkgLfeegvd3d3o6Oiom3LlJBNtYGCg6gVN1TrwY0EXOuQ89vvzaWEFdIoBJ57MXhoup/7153JmQaMWgY4aNMWktWq8HsoQNgQ0gDWwEUURY2NjcLvduOqqq+r+5ikIAoaHh9He3m5qMbI67ToajS4p7RqQYfP444+jv78f3/rWt+r+eJWhBnAKiWVZ3dW5pWpmZgaJRAJXXXVVye8li81IGQ11cgDDMEoWF8uyBVOIKy3SlTGTyZSUiVZpHfixALdHpoKcxebQ/U0JgEqFTjErJ5GUb9jERaWVFjoENEbuNaPlXAQsakso34WWBYrXQ5uCTSLGQBAk3LPrg5LqlwmCgJGREbS0tGDNmjUFX1sPEgQBQ0ND6OzsRE9PT1mfUW7aNXnvY489hu3bt+O55567HGEDNIBTWFYBJxwOY25uDhs2bCjpfSQ5wOl0Ku4Io3iNXgpxZ2cnWltbK+4zJ+P0+Xx1OZM98GNBtnT8zmxCgdc4LEnGH/DbSrJy4qq4kMOefwz0oEOAo2fRqKGjtmoKQcVIatjIj7Pk4lSw4RYzF3hehMiL+Nun5EGo65fNzs7C5XIpPZG0Swd4nsfQ0BCWLVtW9s27miLj7erqsmzlvdm0a0CGzaOPPoodO3bgm9/8Zt1dPxaqAZxCsgo4pNTG5s2bTb+HJAd0d3dj5cqVJVUOIDcHAjqPx4POzk60t7dbvu6BZKKtWLGibstkAMAzf5+Gy22H25P9/pIkWzxaaY+tlte0jttMz5VWDDrJlHyjd7mMJwTqDDEzymSyIHEvrk8yAxs1aADkwEZPJJAeDochCAJaW1vR0dEBj8eDoaEh9PT0WJaVWUlxHIfDhw9j5cqVFe3Wq027bm5uxtjYGG6++WZ85Stfwc6dO3HgwIHLGTZAAziFxXGcJdllCwsLmJiYQF9fn6nXW1k5gPiZQ6EQIpGIUrW5s7NzySme8Xgco6Oj2Lhx45KrMVRDyWQSz/4PwONzQhIl+X/Vea2GT6nQMQucZEqAw5EPGC10kknBcJseVLTPA0A6LT8m1pwZqwYA/vqJ0pJSiXU9MzODcDiMlpYW9PT0mKqNV0sR2KxevdrSNXLFJIoipqam8MILL+B3v/sdfD4fvvzlL2PPnj26iQqXkRrAKSSrgJNIJHDmzBn09/cXfe309DTOnDlTscoBpGpzKBQCx3Flx31IJ8Jt27bVTcJCIc3Pz+Po0aPo6+vDN/8nrUAHANxefauPoqgcCJUKnWRKMLBySrdoXC46DyiFRGBDxDDZagAO1SIijheQTnLgeQEiL+If/qK8rMJ0Oo2hoSGsX78edrtdCaTb7XbF9UbaUtSDSKO33t5edHR01GT/jz76KK655hrs378f//7v/45f/vKXePbZZ3HjjTdWfTxVUgM4hWQVcFKpFI4fP47BwUHD1+glB6jLklcq318d92lpaVFKxxTa38TEBGZmZtDf31/TTDSzCoVCSt0udbzhy/81qbjYyBodr8bFlmfpaB9roaMDk2LQSang4NR5fyolw8LjyQ3Ua6Hi8dgKggYAOHbRmuFIYoD8+L/9WfkwSCaTGB4expYtW/L6RJEJTjgcBsMwiuutubm5ZutxiLtar9FbNcSyLB555BFce+21+Iu/+IvL3Y2mVgM4hWQVcBiGwcjICHbt2qW7vZTkgEpJHfeZnZ2Fz+dTZqYk7kOKGLIsiy1bttRNJlohTUxMIBQKob+/3zB+9fTfJgAALm8uPAl81MdfCxygdOgQgDic+sePQIe8Ti09qBBlMvLr3W7iQsu+n4AGyIXNUkADyO7fI0eOYNu2bUXXXOl1hCWB9GrVVCMV4Dds2FATNzDLsnj44YfxsY99DF//+tevJNgADeAUFs/zlrQV4Hke77//Pq655pq8baStbjnJAZWSXtynra0N0WgULS0tWLt2bd1fKKRgKEnTNjObfvpvExAlCR5ffvVikqzm8TmLWjlAFjrJRLY8klMHMFropFPyilCHI/+1BChAFira5wGAyahBswghjwOJWAYAwHMCREHE//efl3bDnZ+fx7Fjx9Df31+yu0ySJCQSCcX1RlGUYRaXVSJuP6OuopUWwzB45JFHrlTYAA3gFJZVwBFFEe+88w4++tGP5jy/sLCA0dFRpQVCPVZ6BqA0TLPb7aBpuqbrfcxIFEUcOXIEbre7rKKLBDwAcuCjzpDOS5fWyZfWA5EedEiwXk8Ohy0PKERMhodLBR4mo3WfyY95TlD+twI0gFxNgrQwt6KiOsuyiustlUohGAyio6MDwWDQEtcbaWG9efPmktrDWyWGYfDwww/jhhtuwJ//+Z/X5XVTBTWAU0hWAQcA3n77bVx77bXKY5IcsH37dni93rqFjTYTrdy4T7XEcRyGh4fR2dlpunW1kR57PgKXN9fa8fmzj8uFjhFg1DDKpLK1bxyu3EwvLVjYDAenO+uSIqABZMjwnID/+Zx1M/qZmRmcP38e27dvr0gMTxRFzM3NIRKJKGn9xPopp3cOiTGZbWFttRiGwUMPPYQ/+ZM/wZ/92Z/VzbVdAzWAU0iVAA4pZLiwsKCUaCfJAfUEGkBesHr69GnDTDQzcZ9qKp1OY3h4GL29vZamuT72fAQAFPhoXWpa8NAa8Nh13GN6cZ5MitO1gAAgk86FCiCDRq180PD43y9Ym+47NTWFqakpJbGl0pIkCalUKqcyOLGwA4FA0eslkUhgZGQEfX19CAQCFR+vVgzD4POf/zxuvvlmfPWrX62r67sGagCnkARBAM+X1lzKSG+//TauueYajIyMwO12Y+PGjQBQ83iNkUrNRFP75Ench7T6rUZJd2KJbd68uaL+eQIfAPD4sq6kcqDDpFjYdJ4HZGsnk9av8MmxPBxOe85jIOs6S8VS+Je/s36F//j4OKLRKPr7+2uWMKItH9Pc3Iz29na0tbXljYmcE/39/TVJ3c9kMvj85z+PW265Bc8880xdXd81UgM4hWQlcN566y3Y7Xb09PSgp6enLpID9EQy0TiOw5YtW8p2k2UyGaVVNFnv09nZaWpWWqpIdepqrgl68NkpAIDbq4KO5nvZ7PnHzq7TvU0NHSad24OJgEVtvQAAx3Cqv3nwHF8RyADyOXH27FkkEgn09fXVhesUyDbli0QiiEajcDqdioXNsiyOHj1aVkKDFcpkMnjwwQfxyU9+El/5ylfq5vqusRrAKSSrgLOwsIB33nkHu3btquvkAJ7nMTo6ikAgYGkmGon7hEIhJBIJS+M+U1NTuHDhQs2rUxMAAVBm2k63PB4teJg0C5te21BkLSE1UIi4nDRnDi/916XFqMyITEAEQcDmzZvr5lzVUzqdRjgcxsWLF5FIJNDd3Y2uri40NzdXddwENrfddhu+/OUv1/Uxq7IawCkkURTBcQaNS0zq4sWLOHfuHERRxEc/+lFQFFWXsMlkMhgeHsbKlSsrWgPLqrgPmXXHYrG67SB535+dB03TCni0bjY2wxYcN6dqmvOjAx6Ew2Fl/UpHRwfa2toqGkeRJAljY2Ow2+3YsGFD3ZyrhTQ3N4fjx49j27ZtSuuAWCyGQCCguN4qecwymQweeOAB3H777Xj66acviWNWRTWAU0hLAY42OeD999/Hjh07lO314pYAsr7uTZs2IRgMVm2/5cZ9RFHEsWPHQFEUNm7cWFfH0kiktI6ZBZKFJEkS4vG4sn6F1Mbr6Oiw1HUkiiJGR0fh9/vR29t7Sdw4Sar29u3bc7LZjI4ZWfNjldLpNB544AHs3bsXTz311CVxzKqsBnAKqVzgkF4g6uSAQ4cOYc2aNRVrS1uuSCZarXzdapmJ+/A8n9Nn5VK4qMPhsFIfz4o1K2ppS8eQDK6luJFII7K2trYld6mtliKRCE6fPo3BwcGirlVyzCKRCDKZjLLmZynXZjqdxuc+9znceeed+OIXv3hJnJc1UAM4hVQOcEjpDG1yQDQaxeTkJNLpNFpbW9HZ2Vl137JW4+PjStmXequJphf3aWlpwfj4OFatWnVJlL4HqhtjEgRBWSNF3EjE9Wa2ajPHcUrli3puN6FWKBTCuXPnyloXJAhCzpqfclpGp9Np3H///bjrrrsasCmsBnAKSZIksCxb/IWLIpUDtmzZgmAwqJuJRupJhUIhxGKxqjZKIyJ95nmeX1ImWrUkiiKmp6dx4sQJ2O12NDU11XS9j1mdO3cOc3NzNUkjVjcAi0ajcDgcirvSyMoiFZRXr16NZcuWVXW85WpmZgbj4+PYvn37ks8FdcvoSEROfyfw8fv9uiAhsLn77rvxp3/6pxWFjSAI2LVrF1asWIFf/OIXFdtPBdUATiGVAhySHDAwMGC6coAkSZifn0coFFIC6J2dnRUNbBKXVHNz8yXjm1e3FvD7/TVd72NGpN02KXJaD0AnGVyRSES3LQWp6VerCsrl6OLFi7hw4QK2b99ekb47LMsqFmMymcxrsZ1KpXD//ffjM5/5DJ588smKX0s/+MEPcOjQIcRisQZwNLpigEOKRMZiMaVygCRJSjq12ZsNCaCTgplkRtrZ2VlWOQ89VSsTzUrNzMwoINebmWvjPiSAXon1PmYkiiLGxsbgdDqxfv36ugS6tjyRz+dDLBbD5s2bLxnYXLhwAdPT09i+fXtVrEd1i+0f/vCHStX0/fv34xvf+EbFf+fJyUk8/PDDeO655/CDH/ygARyNLgvgAHJpCiOR5ACPx4MNGzYAsK5yQDqdRigUQjgchiRJSpfOcrNqSBn5Sq/Et1Lj4+MIh8MFWwuoxfO8EkAncZ/Ozk7LCkAWEwm2B4NBrFmzpuL7s0LxeBxDQ0NoaWlBIpGAy+VSLEarJjpWa3JyEqFQCAMDAzVJh0+lUnjggQcQDAYRjUYRi8Vwzz334Otf/3rF9rl//34cOHAA8Xgcf/d3f3fZA6d++8TWSEbJAVZVDvB4PFi9ejVWr14NlmURDodx8uRJZDIZJXvLbLXmUCikZEnVOhPNjIhLimEYDA4OmoaF3W7H8uXLsXz5cmVGGgqFcOLEiYrXeSPtilesWHHJBNsXFhYwNjaGwcFBZSKTTCYRiUQwMjICURQVi9EohlFtkfI6tYJNMpnEZz/7Wdx///147LHHQFEUFhYWcOzYsYrt8xe/+AU6Ozuxc+dO/O53v6vYfupJV6yFw7IstN99fn4eR44cKZgcUCkJgqDM4km1ZqNZvCRJGB8fRyQSMW0l1FqCIODIkSPweDxltRbQk9pdSdZhWBn3IfGPtWvX1qRdcTmanZ3FiRMnMDAwYHgMOI5TzrVkMolgMKjEMGoRlzp37hwWFhawbdu2muw/mUzivvvuwwMPPIBHH320agA+cOAA/vEf/xF2ux2ZTAaxWAyf/vSn8U//9E9V2b+FarjUikkLnKmpKZw/f76k5IBKST2Ln5ubg9/vV5IOaJrG8ePHIYoiNm/eXBeB62IiKbnLli1bcmuBQrIy7kOqEV9KrkqyLki7QLKQtBUivF6vYjFWI6X+zJkzSCaTppvpWS01bB577LGq75/od7/7XcOldiWIJAfE43Hs3r277OQAK0XTNFpbW5X6bPF4HKFQCGfPnlUWtG3atOmSgE2lWgvoye12Y+XKlVi5cqVSffj8+fNIJBIlNf4iLqmlVg+opi5evIjJyUns2LGjJItXe66R9OGhoSEAUOBjdbdOUrEjk8mgr6+vJm69RCKBz372s3jwwQfx6KOPVn3/V6KuWAuH4ziwLIuRkRF4vV7LkwOsFnHvLF++HJIkIRwOg6IoxYVUjzEcktCwZcuWmnRjJCKNv8LhsLII0CjuQ1a29/f31006djFNTEwowXYr04jV3TrT6bQlK/eBbCyP5/maFQ5NJBK477778PDDD+ORRx6p+v4vMzVcasUUi8XwwQcfYNWqVVixYkXdthUAjDPRGIZBOBxGKBSqi9RhtUhrgXooraNWobjP/Pw8Jicna16huhSdPXtWiX9UMthOVu6rC42SxZOlFmc9fvw4AGDjxo01hc0jjzyChx9+uOr7vwzVAE4xffDBB+ju7q56ckCpIq60bdu2Fbxxk9ThUCiEZDKJ1tZWS2aj5aheWguYEYn7jI+Pg2VZ9PT0YNmyZXUB7UIirmCGYaq+CFUP2mYKjUqShKNHj8Jut9dsLVM8Hsd9992HRx99FA899FDV93+ZqgGcYuI4DqIo1m0Pm6VkoomiqJTZWVhYUErG6HVPtHrMZ86cQTwer9vWAlqpb9wbNmzA7Oysst6nlLhPNSVJUk5V7Vqfs2YKjUqShCNHjsDtduOqq66qGWzuvfdePPbYYw3YWKsGcIqJ53nlH1BfbQVImX5JkpaciSZJEhYWFpTaWx6PR3EhWZlOLYoijh49CpqmsWnTpprfBM2IjFmvL4xe3KfS5YnMjnlsbKymN+5CIoVGI5EIFhYWlH4109PTaGpqwtq1a2syLgKbxx9/HJ///OdrMobLWA3gFNORI0ewcuVK2Gy2urpoeZ7PWdVudWYQyUIKh8OWrVshddyCwSBWr15dV8fTSOrqAcXGXOn1PqWMWd3Cod5FagqOjY1BEASlwVx7e3tVj1ssFsO9996LJ554Ag8++GDV9nsFqQGcQpIkCQ8//DA+/PBD3HDDDdi7dy+uvfbaihQKLEUkhXjNmjVVqepL4hehUAiCIOSU2TELDYZhMDQ0dEnVcSPrgrq6urBixYqS359OpxUXEs/zSoWISq7a53leWcvU09NTkX1YLW3/nWKFRishApsnn3wSDzzwQEX20VADOKbEMAx+/etf4+DBg3jnnXewe/du7N27FzfddJPlDbWKiaz9qFUKMVl9HgqFTPf2SSaTGBkZwYYNG9Da2lrlEZcnq6sHkPU+JFmjEnEfUl6np6fnkoG6IAgYGhpCZ2enLiC1hUabm5vR0dGhVGy2QqQW2lNPPYX777/fks9sSFcN4JQqnufx1ltv4eDBg/jtb3+LTZs24c4778Qtt9yCQCBQ0X2Tysn1svZDr7eP9mYwNzeHY8eOXVKLIwkgN23aVJHqAdq4D3EhLSXuwzAMDh8+fExFOoUAABmMSURBVEmV1xEEAYcPH8by5ctNWZDE9RaJRBCNRi0pNLqwsIB77rkHX/rSlxqwqbwawFmKRFHEBx98gJdffhlvvPEGurq6sHfvXtxxxx2WlnmXJAnnz5/H7Owstm3bVpc10fR6+zidTszPz2P79u1VtwTLVbWrB5AKESRZw263F22UplU6ncbQ0NAlZUHyPK8UOy3XGiOFRsPhcFmFRglsnn76aXz2s58tawzFNDExgYceegjT09OgaRpPPPEEnnnmmYrs6xJQAzhWiawdOHjwIH75y1/C4/Fgz5492LdvH7q6usr2PZNMNACXTJkaskI8FArBbrfD6XSWfBOthSKRCE6dOlWwoGWlReIX4XAYgiAUjfsQa2zz5s01rdJQiojrb9WqVZbFILWFRltaWhRrW++amZ+fxz333IOvfOUruO+++ywZg54uXryIixcvYseOHYjH49i5cydeffVVbNmypWL7rGM1gFMJEYvklVdewU9/+lMwDIM77rgDe/fuLakCMsdxGBkZQWtr6yWT1SVJEk6cOAGO45SFhuQmGgqFLOntUwmRGmP1tAhVr1qzOu5DKktcSu5K0sZ6zZo1FauZZ1RoNBgMwuPxKLB55plncO+991ZkDEa688478fTTT+OWW26p6n7rRA3gVFqSJCEUCuGnP/0pXn31VczMzOCWW27BnXfeWbDMerUz0awQaS3g9XoN136QuluhUKis3j6VkHrhbK0zEI2kjfs4nU6kUikMDAygqamp1sMzJZZl8eGHH+Kqq65Ce3t7VfapTvH/m7/5G3z44YcQRRGPPfYYvvrVr1b1nDt37hxuuOEGjI6OXjK/mcVqAKfamp+fxy9/+Uu8+uqrOH78OG666Sbs27cP11xzjRJoJy0Qal3MshSRFOLly5ebTscli/9CoVDR3j6VEKkekMlkalb2vhyRZnxtbW1YWFgoK+5TbZGkhnXr1tWsjfXc3Bzuv/9+bNu2DdPT0zh9+jTuuusuPP/88xXfdyKRwI033ojnnnsOn/70pyu+vzpVAzi1VDqdxq9+9SscPHgQ77//Pj7ykY+gra0Nv/rVr/Dmm2/WVTHLQiJB66uuuqrsDKlCvX0qYXUUqh5Qz5qZmcH58+exfft2xfVXatyn2iLdcTdu3IhgMFiTMczNzWH//v34+te/js985jPKuI4fP46BgYGK7pvjOOzZswef/OQn8bWvfa2i+6pzNYBTL2JZFk899RR+85vfoKmpCZs3b8a+ffvwiU98oq5iHVpVorWAurdPNBqF0+lEZ2cnOjo6LImvkJX4zc3NlldpqKQuXLiAixcvYvv27YYQLhb3qbbIZKRSKeZmNDs7i/379+Mb3/hG1a0Lsni8tbUVf//3f1/VfdehGsCpFz3zzDNgWRY/+tGPQNM03n33Xbz88st48803sXr1auzZswe33357zWaIeiJZXZVuLaAuswNAgU85+1xq9YBaaXx8HNFoFP39/aYXPJK4TygUUloFkJIx1YhVpVIpDA0NYevWrTWLWRDY/OVf/iXuvvvuqu//rbfewvXXX58Tr/3+97+P22+/vepjqQM1gFMvOn36NNauXZs32xZFEUeOHMHLL7+M1157Dc3NzdizZw/27t2LZcuW1Wx2fuHCBUxNTVU9q4v09gmHw2BZVnEfmWkTQKoHVKOrqFUilbWTyST6+vrKtlLU630ikQgcDkdF4z7JZBLDw8Po6+ur+IJoI9UaNg3lqQGcS0nk5nPw4EH87Gc/gyRJSrp1b29vVeBDxpBIJNDX11fT1gKkt4+6TUBnZ6dubx+yXqWWcYRSRVLMBUGwvOOlNu5T6qLJQorH4xgdHa1punY0GsX+/ftx4MAB3HXXXTUZQ0N5agDnUpUkSZiensarr76KV155BXNzc7jtttuwb9++JbcqMBIJtNtstrror6IW6e1DOk0GAgEl6SCRSGBsbKyms+1SJUkSxsbG4HA4Kt6ETC/uYwTuYiIxvf7+/prFHglsnnvuOezbt68mY2hIVw3gXC6am5vDz3/+c7zyyis4e/YsPv7xj2Pfvn3YuXOnJVYIaYdwKSxCVff2mZmZAcdx6O3tRXd3d90s6iwkURQxOjoKv99fNctVve9y4z4LCws4evRoTduFRyIR7N+/H9/61rcasKk/NYBzOSqZTOL111/HK6+8gsOHD+O6667DnXfeieuuu66sOmyktcCqVauwfPnyCoy4Mrp48SImJiawfv16ZeV5rXrUmJW2VH8tpc0WLBT3mZ+fx7Fjx2paFojA5tvf/jb27t1bkzE0VFAN4FzuYlkWv/3tb3Hw4EH8/ve/x+DgIPbu3Yubb77Z1I0hkUhgdHT0kioMCRhXD7Cit0+lRDLouru70d3dXdOx6Mko7sOyLE6ePFnTIq3hcBj79+/Hd77zHezZs6cmY2ioqBrAuZIkCALefvttvPLKK/iP//gPrFu3Dnv27MFtt92mu4bmUmwtIEkSTp8+jXQ6XbR6gLq3TyqVUjLeCvX2qZRIjbHVq1dfEqWMyLGbnJxELBZDV1cXli9fXlbcZ6kisHn++edxxx13VHXfDZWkBnCuVImiiKGhIbz88st4/fXX0d7errRW6OjowEsvvYSOjg5cf/31dVsuRaulJDWY6e1TKZF07VqWfSlH4XAYZ8+eRX9/PxKJhJKwUekqEdox7N+/H9/97nev1LUtl5IawGko206ApFsnEglQFIUf//jH2Lp1a81dTWZkZfUAvd4+JHBudS+iVCqF4eHhmq7EL0ehUAjnzp3D4OBgzjEpJe5jxRj279+PF154AZ/61Kcs/eyGKqIGcBrKShRFfO1rX8OFCxdw3XXX4ec//zkSiQQ+9alPYe/evdi0aVNdwqecwqFmJUkSEomEcgO1slAmWa9yKaVrA8D09DQmJiawffv2ogCu1HqfmZkZ7N+/H3/1V3+F2267rezPaaiqagCnoax+8pOf4OjRo3j++eeVm0EkEsHPfvYzvPLKK5icnMQnPvEJ7Nu3D4ODg3VRXbna1QPUvX1EUURHR0dZvX1IZ9FarlcpR1NTU7h48SIGBgZKdpdp1/u0traio6Oj5LhPtWDz+uuv45lnnoEgCHj88cfx7LPPVmxfV4gawGkoK0mSCs464/E4XnvtNRw8eBBjY2O4/vrrsW/fPlx77bU16SNT6+oB5fb2mZ2dxYkTJ2qaQlyOJicnEQqFMDAwsOS4lt5C3Y6OjqJxHwKb73//+/jkJz+5pDEUkiAI2LBhA95880309PRg9+7deOmll67UTp1WqQGchsoTwzD49a9/jVdeeQV//OMfsWvXLuzbtw833XRTVZIMiIVQL+4os719wuEwzpw5g+3bt8PlctVwxKVpYmJCSTO3OolCkiTEYjGEw+GCcZ/p6Wncc889ePHFF3HrrbdaOgat/vCHP+D555/HG2+8AQB48cUXAQAHDhyo6H4vczWA09DS9X/bu/egqMo3DuBfkJhwhvBCKLoqKDGAyE1IU0HiMhDupaYCdEwcYPyrRnPSbPynnAlHJUYnGy1NLRKchN0FhQEJsAJNAuUiuAqJ3EFg0LjFZff8/uh3Nu+CcM677D6fv8RxOM/sIN9z3vO87zM6OoqioiIolUoUFhbCxcUFCoUCoaGhgoRBd3c3amtrDfYJ4WmzfUZGRvTjBSa7+UBIDQ0N6OnpgYeHhyjLqA++9+nq6kJBQQGCg4OxZ88e7Nu3T5TxzGlpacjJycHx48cBAMnJybhy5QoOHz4s+LWN2JgDxzDn7hKDYGFhgcDAQAQGBkKn0+Hq1atIT09HUlIS7O3t9e3Wk9Hy297ejsbGRvj4+BjsMTXm5uaYNWsWZs2ape/aqqurw7179zBjxgx0dHTAzs7OYOt/UH19PXp7e0ULGwCwsrLCwoULsXDhQty7dw/V1dXYuXMntFotsrKyYGFhAX9/f0GXcZ90g22IDTPGiv3bYSOWmJgIMzMzdHV1sS5lwszNzeHr64u9e/eirKwMBw4cQFdXFyIjIyGVSnH06FG0trY+8T/08zQ2NqK1tdWgw+ZRZmZm6O7uhrm5OdauXQsXFxeMjo6ioqICf/75J+7cuYOBgQHWZT6G30A70bEIEzU4OAilUokjR46gpqYG4eHh+Pnnn/H7778Lel2JRIKmpib9183NzQZ5+oOxoiU1gTQ1NSE+Ph4ajQZlZWWwtbVlXZIgOI5DQ0MDVCoVMjIyMDQ0pB+t4OTk9My7R/6X38DAANNffuPFcRzq6uowNDQENze3x+qeyGwfIfF1Dw8Pw83NjVktbW1teP/993HgwAEEBweLeu3R0VE4OzsjPz8f8+fPh5+fH1JSUrB06VJR6zAy9A6HNf6wQYVCgdLSUqMNnAdxHIfOzk6o1Wqo1Wp0dHQgNDQUCoXiocmIwL/vQzQaDczNzQ1uJMKzcBwHjUYDMzOzMdU9ntk+QuJn8Oh0Oqb7rviwSUxMRFBQEJMasrOzsW3bNmi1WsTGxmL37t1M6jAiFDgsZWZmIj8/H4cOHYKDg4PJBM6j7t+/j6ysLKhUKty8eROBgYGQy+Vwd3fHRx99hJ07dzK90x4vfkqrlZUVlixZMu66nzXbR8hjdviQNDc3h7OzM7PPu7W1FZGRkfjqq6/w5ptvMqmBCIICR2ghISFob29/7O+//PJLJCQk4MKFC/rjWEw1cB40ODiIvLw8pKamIj8/H2+88Qbi4uIQEBAwJd7b8EfszJgxAw4ODhP+fg/O9unu7sbLL78MOzs72NraTurnwQ98s7S0fO4Sp5D4sElKSkJgYCCTGohgKHBYqaqqQnBwsH5QFf9SsqSkZErNnBFCW1sb3nnnHXzyySeYOXMm0tPT8dtvv2HZsmWQy+UICQkxyN35fDPAnDlzJv2IHV5/fz/u3r07qbN9+Cey6dOnY/HixczCpqWlBZGRkTh48CDWrl3LpAYiKAocQ0FPOP85fvw4XnvttYd+6eh0OpSUlCA9PR15eXlYtGgRpFIpIiIimJwy8KiRkRGUl5dDIpHA3t5elGvys306OzsxOjr6QueU8dNFra2t4ejoKHDFT9fc3IyoqCgKG+NGgWMoKHDGjr8jT09PR3Z2NmxsbCCVSiGTyTBnzhzR79CHhoZQXl6OxYsX49VXXxX12rwnzfbhzyl72ueh0+lQWVmJmTNnYtGiRSJX/B8+bA4dOoSAgABmdRDBUeCQqY3jONy+fVs/WoHjOH27taOjo+DhMzg4iIqKCoOaiDqW2T78KGtbW1ssWLCAWa1NTU2IiorC119/DX9/f2Z1EFFQ4BDjwXEc2tvboVaroVKp0NPTg/DwcMjlcri6uk56e3F/fz8qKyvh5ub2xImphuBJs31mz56NtrY2QcY5jAcfNocPH8aaNWuY1UFEQ4FDjFdPTw/OnTsHlUqF+vp6BAUFQSaTwdfXd8LtxX///Teqq6un3Pjt+/fvo6qqCmZmZpg+fbpgw9Gep7GxEdHR0fjmm2+wevVqUa9NmKHAMXU7duzAuXPnYGlpiSVLluDkyZNTavLkWPX39yM3NxdKpRLl5eVYvXo15HI51qxZM+6DNHt6enDz5k14eHjouwynAr6xYcGCBZg7d+6kzfYZr4aGBqxfv57CxvRQ4Ji6CxcuICgoCBYWFvj0008BAPv27WNclbCGh4dRWFgIpVKJ4uJieHt7QyaTITg4+LntxV1dXfjrr7/g6ekp+lPBRIyMjODatWtwcHB44qC6F53tM14NDQ2Ijo7GkSNHsGrVqkn7vmRKoMAh/1GpVEhLS8Pp06dZlyIarVaLS5cuQaVSIT8/H05OTpBKpQgPD3/svUxHRwcaGhrg5eU1JTah8oaHh1FeXg5HR8cxddGNdbbPeN25cwfr16/Ht99+i5UrV77w9yFTFgUO+Y9MJkNUVBQ2btzIuhQmdDodKioqoFQqkZOTg9mzZ+tHK5w5cwY6nQ4ffvghk+mmL4pv2XZycnqh8RBPm+3zvMmcj2IRNqayXDyFUOCYgmcdr6NQKPR/Li0thVKpnDJnlgmJ4zjU1tZCqVTi2LFjmDZtGmJiYvDee+9BIpFMic/on3/+QXl5+aS1bPOzfe7evYvu7m5YWlrqmw6eNb2UD5vvvvsOK1asmHAdY2WKy8UGjgKHAD/88AOOHj2K/Pz8KfUSXGgcx2HPnj24ceMGEhISkJWVBbVajb6+Prz11luQyWRMT1R+Fn5/kIuLi2B39QMDA/pjdgDomw4e/Bmqr6/Hhg0bcOzYMbz++uuC1DEWprhcbIAocExdTk4Otm/fjl9//ZXZLnlD1dnZicTERCQkJDzURt3V1YXMzEyoVCo0NzcjJCQEcrkc3t7eBjGrZ2BgAJWVlXB1dRVtf9CDs31u376NoqIiBAQEYN++ffj+++/h5+cnSh1PY+rLxQaCAsfUOTk5YWhoSL++v3LlShw9epRxVVNHb28vsrOzoVQqUVNTA39/f8jlcqxatYrJux5+M+rSpUvxyiuviH594N9xEydOnMCpU6cAABEREXj77bcFGQtNy8VTCgUOIZNlaGgIv/zyC1QqFf744w/4+vpCLpcjMDBQlBbqvr4+VFVVwd3dHdbW1oJf72nq6uqwceNGnDhxAh4eHrh48SLUajXWr18v+vE1tFxsUChwCBHC6OgoioqKoFQqUVhYCBcXFygUCoSGhgoSBr29vbh+/To8PDyYjm6ora3FBx98gJMnT2L58uXM6gBoudgAUeAQIjSdToerV68iPT0dubm5sLe317dbv0ir8qPu37+PmpoaeHp6Mr2Lr62txaZNm3Dy5En4+Pgwq4NHy8UGhwKHsJWTk4OtW7dCq9UiPj4eu3btYl2SoDiOw40bN6BUKpGVlQUrKyusW7cOcrkc8+bNG/c7hnv37kGj0cDT03NCQ9gm6tatW4iJiTGYsCEGiQKHsKPVauHs7Iy8vDxIJBL4+fkhNTUVbm5urEsTBcdxaGhogEqlQkZGBoaGhhAREQG5XD6mMc/8mW5eXl5Mj9nhw+bUqVPw9vZmVgcxeBQ4hJ3Lly/j888/R25uLgBg7969AIDPPvuMZVlMcByHzs5OqNVqqNVqdHR0IDQ0FAqFAsuWLXus3bq7uxt1dXXw8vJ65qZLod28eRMxMTH48ccf4eXlxawOMiWMOXDYby4gRqelpeWh4V8SiQQtLS0MK2LHzMwMdnZ22LJlC7Kzs1FQUAAPDw8kJSVh1apV2LVrFy5dugStVou0tDSoVCp4e3szDRuNRkNhQwRBgUMm3ZOemmmfxL9sbGywYcMGnD17FleuXEFISAiSk5Ph4eGBL774AjNnzmRan0ajwebNm5GcnExhQyYdBQ6ZdBKJBE1NTfqvm5ubMW/ePIYVGSYrKyvI5XJIpVJIJBIkJSXh8uXL8Pf3R1xcHDIyMtDf3y9aPTdu3MDmzZvx008/wdPTU7TrEtNB73DIpBsdHYWzszPy8/Mxf/58+Pn5ISUlBUuXLmVdmsHp7u5GTEwMUlNT9ft4dDodSkpKkJ6ejry8PCxatAhSqRQRERGCPQHV1NQgNjYWp0+fxrJlywS5BjFa1DRA2MrOzsa2bdug1WoRGxuL3bt3sy7JYHEc99QlR51Oh+rqan27tY2NDaRSKWQyGebMmTMpS5UUNmSCKHAIMTYcx+H27dv6dmuO47Bu3TrIZDI4Ojq+UPjwYZOSkgJ3d3cBqiYmgAKHEGPGcRza29uhVquhUqnQ09ODsLAwKBQKuLq6jul06+rqasTFxVHYkImiwCHElPT09ODcuXNQqVSor69HUFAQZDIZfH19HxrBwOPDJjU1ld6tkYmiwCGkqakJmzZtQnt7O8zNzbFlyxZs3bqVdVmCGxgYQE5ODpRKJcrLy7F69WrI5XKsWbMGL730Eq5fv474+HicOXNG9NMfEhMTsWPHDnR2dsLW1lbUaxPBUOAQ0tbWhra2Nvj4+KC3txfLly+HWq02mSN2AGB4eBiFhYVQKpUoLi6Gg4MDbt26xeRzaGpqQnx8PDQaDcrKyihwjMeYA0f8SVKEiMTe3h729vYAAGtra7i6uqKlpcWkAsfS0hJhYWEICwuDVqvF2bNnYWNjw+Qz+Pjjj7F//379ADVieihwiEm4c+cOrl27hhUrVrAuhZlp06YhOjqaybUzMzMxf/582lBq4ihwiNHr6+vDu+++i4MHDzIbz2wKnjUWOiEhARcuXGBQFTEk9A6HGLWRkRFIpVKEhYVh+/btrMsxSVVVVQgODtYPkeOPOiopKcHcuXMZV0cmATUNEMJxHGJiYjBr1iwcPHiQdTnk/xwcHFBaWkpNA8aDxhMQUlxcjOTkZBQUFMDLywteXl7Izs5mXRYhJouecAghhEwEPeEQQggxLBQ4hBBCREGBQ4iItFotvL29IZVKWZdCiOgocAgR0aFDh+Dq6sq6DEKYoMAhRCTNzc3IyspCfHw861IIYYIChxCRbNu2Dfv37x/TrBpCjBH95BMigvPnz8POzg7Lly9nXQohzFDgECKC4uJiZGZmwsHBAdHR0SgoKMDGjRtZl0WIqGjjJyEiu3jxIhITE3H+/HnWpRAyGWjjJyGEEMNCTziEEEImgp5wCCGEGBYKHEIIIaKgwCGEECIKChxCCCGioMAhhBAiCotx/vsxdyMQQgghD6InHEIIIaKgwCGEECIKChxCCCGioMAhhBAiCgocQgghoqDAIYQQIgoKHEIIIaKgwCGEECIKChxCCCGioMAhhBAiiv8BxJ5HMF2XAQoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_scalar_field(u, -5, 5, -5, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2 Plotting a scalar field as a heatmap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 504x504 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def scalar_field_heatmap(f,xmin,xmax,ymin,ymax,xstep=0.1,ystep=0.1):\n",
    "    fig = plt.figure()\n",
    "    fig.set_size_inches(7,7)\n",
    "\n",
    "    fv = np.vectorize(f)\n",
    "\n",
    "    X = np.arange(xmin, xmax, xstep)\n",
    "    Y = np.arange(ymin, ymax, ystep)\n",
    "    X, Y = np.meshgrid(X, Y)\n",
    "    \n",
    "    # https://stackoverflow.com/a/54088910/1704140\n",
    "    z = fv(X,Y)\n",
    "    \n",
    "#     # x and y are bounds, so z should be the value *inside* those bounds.\n",
    "#     # Therefore, remove the last value from the z array.\n",
    "#     z = z[:-1, :-1]\n",
    "#     z_min, z_max = -z.min(), z.max()\n",
    "\n",
    "    fig, ax = plt.subplots()\n",
    "\n",
    "    c = ax.pcolormesh(X,Y,z, cmap='plasma')\n",
    "    # set the limits of the plot to the limits of the data\n",
    "    ax.axis([X.min(), X.max(), Y.min(), Y.max()])\n",
    "    fig.colorbar(c, ax=ax)\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('y')\n",
    "\n",
    "scalar_field_heatmap(u,-5,5,-5,5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.3 Plotting a scalar field as a contour map"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Gp43NzVVsaaniq5Zqmtx2AGLVOkYlZ3FW7hBGJmUyLDGjT209ngiSJJGqjyFVH8P0jKJjr1u9bnabG9jdXs+O9no+qj3AGxU7Acg0xDIhNY9JqflMTssnwxAbLff7BMK9HLQzUcQ/gvB8jvCsDgum/VEk061I+rMQvh0IzwfI05R/IwtmH0cIH8L+ILiWhkvbxf8TSdm9kXqeoIs1zW+xpf1jlJKKOWmXMSXlbDQRLlQdCdwBP1+1VLOusZyNzRVU2s1AONhlQmouE1PzGJucQ3FcCgp5RfSjiNfqmZ5RdExEQ0Jw2NrC1rYavm6pYW1DGcur9gLQLzaZqWkFTMsoYmJqXp+Nzo0EQnggUI2U8GT4BWU+KJMJWX8JioSwWAoBilQINiOCrUjKlKj63FOQ77I+jAg2Iaw/A/9uMFxzdAtW3W32QyLELstaPmt6DWfAxuiEWZyafhkx6oRu86EraHJ18GXDEVY3HGFLSzXeYACdUsXE1DwWFo1hclo+/eNS5C3DLkYhSQxKSGNQQhpXFo87JqCbmivZ2FzJsoqdvHJkKzqlislp+czO7M/szGJS9L13m/v9uqcpMA5hePwpEbufJEmH0IwB9wqE/pzwEY3/MPh3ISUuPXqNhPCsBIL/UyyF8EXlOCfayGeYfRTh/Rphux2EFynuISTd3G613+iu5IP656hxHSbHUMxZmdcdS+LuDVTZzXxad4jP6w6z29wAQK4xnpmZxczM7Mf4lFx5VRNlPAE/X7VWs7ahjC8byqh32ZCAkUlZnJY9gDOyB5Fjio+2m8eNJ+jixYrf0+CuoMA4hLOzridNlxsRWyJQhrA/CqEW0EwDYQYhUMT9MfxzEUS0TkFKeBFJPQQh/Mcm28J/AOFaBv79SIbLkAwXRsTH7kIO+umEk0EwhRDgWhLehlXmISU8iaQq+uE3dhHeoJvVzW+wpe0j9EoTp2dcyciEGSh6QNH2H6LWYeWj2gN8VHOAA9ZmAIYnZnBa1gBmZ/WnODZZXkX2UIQQlNpa+aK+lM/rD7Pf0gTA0IR0zswdzFk5g8k0xkXZyx8mJIJsM6/i86aleINupqacy8y0BRE7vhCBGiRVLiJYj7A/hiL+YYQQ4Uj6YC2KhCcRIhiuVQsI73qE600kzQTQjEPYH0GKvTcqkfZdhSyYndDXBVMIH6Lj9+B+L1w0Pe7hbu1ZedBWwsqG5+nwmxmbeCpz0y9Hr+rZ22NWr5uPag+wvGovO9vrARiVlMW8nEHMzR5IVi94yMr8N7UOK5/UHeTjmoPstTQCMC4lh/PyhjEvZxCxGl2UPfx+nIEOPmtcwnbLahLUqZyTfQP9Y0ZHxJYQAoQFYb0LhAdUuSAEUswvkJTpx7ZfRaAC4X4PSZGIZLwWgFD7BUimXyJpJ0fEt+5AFsxO6MuCKYJtCOut4N8JxtvCDZ67aVXn8FtZ2fAC+2ybSdPlcl7WzeQaB3SL7Z9CIBRiQ1M571TuYXVDKf5QiP5xKZyXN5QzcweTbew923gyP0y1w8KHNftZUbWPcns7GoWSOVn9ubBgBFPTCnp0vmulYz8r6p+h1VvPiPhpnJl5LUZV5CKEheczQA3aKUjSd1e1wr0c4S8NVwRS90f494eLHRhvQFLlRcynSCMLZif0VcEU/kPhnKqQGSn+YSTd6d1jVwh2WdfxUcNL+ENeZqQuYFrqeT22OHqd08qbFbt4t3I3zW4HiVoD5+YN5fz8YQyKT5O3W/s4Qgj2Whp5r3IvK2v2Y/W5yTDEsqBgBAsKR5LZQ1NVAiE/a1veZX3re2gVBs7Ouo5hcVMifr+KYBN4PgP9fCRFLMLxLCAdqwQkXEsRwSYk/UVIqpyI+hJJZMHshL4omMKzJtxpXTIhJTyDpB7SLXY7/Gber3uGw/Zt5BoGcH72raTosrvF9o8hGAqxvqmc18q2s66xHEmSmJZeyEWFI5mZUYxG2XtzQGV+Ot5ggNUNR3irYhcbmyqQJIlZmcUsLBrN1PTCHpkS1OSu5r26J6l3lzEkbiLnZN2ASRXZ3RDh+RxJdxoAofaFSKYbkbTTwoUPPF8gqQcj6c+LqA+RRhbMTuhrgilcSxEdfwqXuEt4ptuaPO+xbuSD+ufwh3yclr6QScnzelzxAbvPw9uVu1lyZBs1TispOiMXFY7kksJRvSL4Q6b7qHVYebNiJ29W7MLsdZFvSuTK4rFcUDAcUw8r0RcUQTa2rmB18xtoFQbOy76JIXETI25XCH+4lJ4wIxmuRdh+gaQ7F3Rzo95c/kSRBbMT+opgChEKt+NyvQjaWUhxjyIpIt9M2R1w8EH9c+yxbSTH0J8Lsn9Giq5n1ZqsdVh5pbSEtyt34wz4GJucw5XFYzktewBqRc8SdZmehTcY4LO6Q7xaupVd5gZMai0XF47k6uJxPW6S1eyp4Z3af9HgrmBUwkzOylwU8YbqImRHdPwBCCCphvSZIu2yYHZCXxBMIXwI2z3g+QgMC5Fifnss5DuSVDj28k7tv7D7rcxKu5hpqfNR9qBV5QFLE88e2sLHtQdRIHFW7mCu7j+eYYly/0GZH8+u9npeLi3hk9qDAJydO4QbBk5iQHx02t/9L4IiwJrmt1nb8i7x6mQW5N5OnnFQxO32taIFsmB2Qm8XTBFyIKy3gO8rJNOvwHhdxA/+gyLA6qY3WN+6nCRNBgty7yDb0HNyrra21vDUgU2sb6rApNJwab/RXF08jvQeGsAh07uod9p4pbSENyp24gr4mZ1ZzM2DpjAquefsrNQ4D/NW7T+x+lqZmbaAGakX9qjJbE9HFsxO6M2CKYJtCMt1EChFinugWw7aLb4W3qz5O7WuI4xNnMOZmdeiUUQ/f00IwVct1Ty+fwNft9aQqDVwbf/xLOw3psfn18n0TqxeN0vKtvFK6VasPjdT0gr4+ZBTGJvSM6JDPUEXK+ufZ5d1HfnGwVyUcwdxmuRou9UrkAWzE3qrYIpAHcJyDQSbkRIeR9JOj7jNA7avebfuCYQQzM++hWHxPSMxeWtrDf/Yu46vW2tI1Zm4YdAkLikchV7VfTVyZU5enH4fr5fv4PlDX9HudTI1rYDbh05jdHLPiBDfaVnLB/XPoZLUXJjzcwbEjom2Sz0eWTA7oTcKpgiUI8xXg3AjJTyHpIlMtY9vCIoAnzUuYVPbSrL0RVyS+0sStekRtXk87DM38sjetWxoqiBFZ+SmQVO4tGiUXM9VJiq4A36Wlm3n2UNbMHtdzM4s5s5h0xkYH/2I0VZPPW/UPEKTp5rpqRcwO+0SeYv2e5AFsxN6m2AK/8HwyhIJKeFlJPXAiNrr8Jt5o/oRql2HmJB0BvMyrkaliO7Krdph4dG9a/mw5gDxGj03DprEFf3GyitKmR6B0+/j1SNbee7QFhx+L+fmDePOYdOjXlLRH/LyYcOLbDOvotA4lIvz7ox4zmZvRRbMTuhNgin8exHma0HSIyW+iqQqiKi9KucBllU/gjfoZn72LYxIOCWi9n4Iq9fNkwc2sqRsGypJyTUDxnPDgInEyGeUP4gQApfPj8vrw+Xz4/YH8PkD+IJBAqEQoZAgdPR7r5AkFAoJlUKBRqlEo1ahV6swaNQYtBoMGrVcAek4sPncPHNwC6+UlgBwTf/x3DxoctTv1x3mNayofxaDysRleXeTY+gfVX96IrJgdkJvEUzh24mwLAJFPFLCYiRV5M5HhBB83f4pHzW8RIImlYX590SspdDx4A8Feb1sB4/tX4/d7+XC/OHcMWw6afqYqPnUExBC0OHx0mDpoNFqp9nmoMXuoN3uos3uxOJyY3G6sbk9ODy+Y4J4oigkiRidljiDjniDjgSjnuQYI8kmI6mxRtLiTGTEx5IZH0OsXp7MNLg6eHTvWpZX7SVRa+AXQ6dzceHIqNarbXBX8nrVX+kImDkn6wbGJs7pFrsiUAnC1W3Vx34qsmB2Qm8QTOHbcVQsk5ESFyMpI5dHGAj5WdnwPNvMqxgQM4aLcu9ApzRGzN7x4PT7mPPx0/SLS+b/Rs7pEWdC3YnHH6CipZ2KFjMVrRZq2i1Ut1mpNduwe7zfuVYhSSSZDCSZDCQa9cQb9cQb9MTotMToNBi0agwaDTq1Cp1ahVqpRKVUIEnSsdJvISEQQhAIhvAFgngCAbz+AC6fD6fXj93jxe72YnV5sLrcmJ1u2h1OzA73f4lyrF5LTmIcuUkJ5CfHU5CSSGFqIgUpiejUJ9dZ815zIw/sWkVJaw2D4lO5b/RcxqVEbyLqCth5s+ZRyhy7mZh0BvMyr4lozWchBMJ8KQTKkBJfRlIPi5itE6XXC6YkSQOAN7/1UiHweyHEP791zQxgBVB59KX3hBD3f9+4PV0w/y2WKUfFMnLBNs6AjaVVD1PtOsj01AuYk3Zpj+lZ2ey2k6oz9fmtwHaHi/11zRxoaOFQYwuljW3UmK1885VUKiQy42PJS04gJzGO7MQ4MuJjyIiPJT3ORJLJELWVSzAUos3uotlmp9Fmp8HSQZ2lg5p2K7XtVuotHd/Z9s1NimdARjIDM1IZlJnKkKxUEk2Rr04VTYQQfFJ3iAd2raLR1cG5eUP59YhZpEZptyQognzeuISNbR9QaBrGpbl3YVBFzpdwdP+VEOro0aLZ6wXz20jhMjb1wAQhRPW3Xp8B3CWEOOt4x+rJgil8uxGWq7tFLJs9NSypfAB7wMoFObcxPH5qxGzJhPEHgxxsaGVXdQO7axrZU9tEg7Xj2M9zk+Lpn57MgPRkitKSKEpNJDcpAY2qd0Y3+gIBqtuslLe0U9bczpHmdg43tlJrth27JjshlmE5GYzKy2BkXiYD0lNQKXvGpK0rcQf8PH1wE88f+gqNUsUvh01nYdGYqE12dpjX8H7908SrU7iy4P9I1mZGzJYI1iPMV0DIHo7FUA+OmK2fSl8TzNOA+4QQU/7j9Rn0EcEU/v0I85XhM8vEpREVyyP2XSyrfgS1QsMV+feSbSiOmK2TGX8wyL66Zkoqaikpr2V3TSNufwCAjPgYRuRkMCwnnaHZaQzMSMGk61lFviOF3ePlYEML++qa2VvbxO6aRpo7HAAYNGpG5mUyvjCbCYU5DM5K61MCWmk384ftn7KxuZIRiZn8Zew8BiVE58ihynmQpVV/RRBiYd49FJgid84oAnUI88Jwalzia0jqnhV41NcE8yVghxDiif94fQbwLlAHNBAWz/3/4/03ADcA5Obmjqmurv7PS6KK8B8J30ySASlpKZIyciW3tplXsaLuGVJ1OVyR/3/Ey5VAupR6i42NpVVsLK3m6/JanF4fAP3TkxlXkM3o/ExG5WWRFmeKsqc9i0arnZ3VDWyvqmd7ZR1HmtsBiNFpmVCUw9T++Uztn09GfO8P/BJCsLLmAH/e+QVWn4sbBk7iZ0NOiUo+sdnbxOKqBzD7mjg/+1ZGJkSuIIoIVIefc4SQEl9HUuVHzNaPpc8IphSu8NsADBFCNP/Hz2KBkBDCIUnSPOAxIcT3Lpd62gpTBGrCB+NIR2+iyAQFCCFY3fwGa1reptg0kkvy7op4ZwOAZeU7GBSfxtCEDFQ9uKv9TyUUEuypbWT1gXLWHaqgvMUMQGZ8LFP65zGpXy7jC3NIMOqj7Gnvot3hoqSili1Hath0pJommx0ITzymDyxg1uB+DM1KQ6HovWfcVq+bB3ev4p3KPRTGJPHX8WdFpVqQO+BgafXDVDr3cWr6ZUxPuSBisQMiUIZoXwiSDilpGZIyclvBP4a+JJjnArcKIU47jmurgLFCiLbOrulJgimCTQjzZRByICW9jqSKTEHzoAiyou4ZtltWMyZhNudm3xjR6DgIt9i66+sPiFFr0SpVxKq1/GnsvD4hmsFQiG2V9Xy+7wir9h+hze5CpVAwpiCL6QMLOaV/PgUpCX0+YKm7EEJQ3tLOhsNVrDtUyY7qeoIhQVqsidlD+jF3WDGj8jKjmrZxImxsquDerR/R5LazaMAEfjF0erevNgMhP+/VPcFu6wYmJJ3BWZnXRqy/rfAfCJ9pKpKQEpchKZMiYufH0JcE8w3gMyHEy//jZ+lAsxBCSJI0HngHyBPf84F6imCKkDW8PRFsOHoQPjwidnwhL29U/53D9m3MTL2I2WkXd8uDfF1jOUvLtvPcKRfmgTAjAAAgAElEQVRh93m4q2Ql87IHcVr2gF5ZoUcIwe6aRj7cdYjP9x2h3eFCr1YxdUA+cwb3Y9rAAjkHsZuwujysP1TBqv1lbCytwhsIkhJjZO6w/pw1ciBDs9N63WTF7vfy4K5VvFmxi+LYFP4+8RyGJHRvOcqQCPFZ4xI2tq1gaNwkFuTcEbEqX8K3HWG+BlSF4TNNRXSPKPqEYEqSZABqgUIhhO3oazcBCCGekSTpNuBmIAC4gTuFEJu/b8yeIJhCuMM3i38vUsILSNpJEbHjDjpZUvkANa5DnJ11PROSTo+IHQgLyrcfUrvb61lStp17hs8iRW/i/aq97Gpv4OLCkVELcvgp1FtsrNhxkA92HKDWbEOrUjJ9YCGnD+/PtAEF6DW9T/z7Ek6vj/WHK/l0TynrDlXiDwbJT07gnNGDOGfU4F535rm2sYx7Sz7C4nPxi6EzuG7AhG5fOW9s/YBPGl+hyDSchXn3oFVG5jhBeNchLDeDZmz4ORjF/pp9QjAjQbQFU4gAwnobeNcgxT+GpIuMiDkCVl6p+BMt3louzPl5xNJG9pkbGfqtBs3fCOeW5iq+qC/lzNzBjEnOxhXwcd/2z5iTVczc7MjWwz1RfIEAqw+U807JXr4qr0WSYHxhDmePGsSpQ/qdNNGsvY0Ot4cv9pXxwc4DbKusR5JgUr88Lhw3lFmDi1Are0d6jsXr4rfbPuHTukNMSM3j7xPOIaObe7vutKzhvdonydQXcVXBbyOWqyncKxC2X4HuDKS4fyBFKQ9cFsxOiKZgCiEQHfeB+w2kmN8jGS+PmK0mdxWvVP6ZC3JupThmVJePv6bhCH/bsxaDSs3U9AKmp/djVHIWgVAIlUKBNxjgwV2rKYpNYl7OIJJ0Rh7fv4FKu5lHJ577XyvSnkCd2cabX+9h+fb9WJxuMuNjmT92COeNGUxmvNyMujdRZ7bx/vb9LN9+gCabnSSTgQvGDmXBhGG94m8phODdqj38ccdnaBQqHh5/FrOzujcV46CthGU1j5CszeLagvswqSNTuF04X0TY/wqGq1HE/iYiNn4IWTA7IaqC6XgG4XgUjDegiLkr4vb8IR9qRdduc9h9HmI0Oh7ctZriuGTOzh3CsvKdrG0s49mpC9AqVcdE88uGI2xuriLXFM+VxeP4ov4w21rruGfErGNl2aKNEIKvy2tZvGkH6w9XopAkZg4qYsH4YUzul9erozBlwgFaG0ureKtkL+sPhQuCzRxUyBVTRjO2IKvHTdr+k4qOdm7fspwD1mau7T+eXw2fhaYbV8pl9t28VvUQcZpkri38A3Hqrg/QEUIg7H8B12KkmN8iGa/schs/hCyYnRAtwRTuDxG2O0F3NlLcIz3+i/qfNLk6uG3zewxPzOT3o09j4ZrX+PPYMyiIScIbDHBPyYcUxSbxsyGn4AsG0SiVhIRgZ3s9D+5aRarexNbWWv4x8VymphdG++PgCwT5ePchXt24g9KmNhKNei6aMJwF44eRHte7zr1kjo8GSwdvlezh7ZK9WF0eBmWmcvXU0cwd3r9Hb9d+s1uzpGwbIxMzeXzKBWR24xZtlfMgiyv/jFEVx6LC+yOSuy1EEGH9OXhXIcU/gaQ7tcttfB+yYHZCNART+HaEq/ioR4TrKUbxcPun0uZxcvuW5UhI/H3iOTx9YBMKScHvR4ezfXa21fOHHZ/yxqwrj0XBfiOc1Q4LFR1tTEzNj3qErNPr4+2SvSzeuIPmDgfFaUlcNXUM80YMQHuSFQc/WfH4A6zceZDFG3dQ0WomIz6Gq6eO4fxxQzH04CCuj2sP8uuSD9EolPxz0nndOvGscR7mlco/YVDFcF3h/cRrUrrcRjgY8grwl4bT7NRDu9xGZ8iC2QndLZgiUIswLwApBinpLSRFQrfZ7krWNpaxqr6UYQkZHLa1ck3/8Vy/4U3emHUl8Vo9dp+HP+/6gjNzBjMto4h1jeWU2lq5fuDEaLsOhANClm7exZJNO7G5PYwvzGHR9LFMKc7rdat9ma4hFBKsP1zJi+u3sqOqgQSjnqumjubSiSN6bGBXRUc7t25+l7KONu4aNoMbBk7qtvu31nWElyv+iFEVw6LCP0VmpRlsQ7RfCASQkt6JaInQb/NjBLN3Zvv2AkTIgbDeDCKAlPBcrxVLgFSdiVi1jsEJ6TS77QREkOK4FJ45FM7iidHo8AaDZBvDgQG5pgSuLD6u+y+i2D1enlq1hdMefoknVm1hVH4my26+hJevv5Cp/fNlsTyJUSgkZgwqZMmNF7P4xosYkpXGPz/bxGkPv8Tza0uOlTXsSRTGJvHO7Ks5PXsgD+9Zw8+3LMcV6B4/cwzFXFN4H86AnZcq7qPDb+5yG5IyGSnhWRBOhOUWhHB3uY0TRV5hRgAhQgjrreBdezTXcsoPv6kH8/SBTRTGJjE3eyB3f72SXe31jEnOZr+libPzhtLgsrGnvYF/TT6fLGNctN3F7fPz+pZdvLhuGza3h9mDi7h59kQGZaZG2zWZHsze2iaeXv0V6w5XkmjUc92M8VwyYXiP264XQvDcoa/4254vGRSfxrNTF5DZTd+7GudhXq78I3HqJK4r+hMmVddHzwrPl+HFhm4eUtyjEZ/YyluyndBdghmy/xOcT0Ut6qur+aT2IB/XHsTqc9Po6sCgVPPY5Pmk6Ey8XbGbaoeFnw2ZSpIuus2nA8EQy7fv58lVW2i1O5k2oIDbTp3EkKzeUyxBJvrsqWnk8S82s7mshvS4GH526iTOHjWox5XfW9NQxh1fvY9OqeLZqQsYmRS5xg3fptKxn1cr/0SSNpPriv6EPgJN54XjWYTj70imO5FMN3X5+N9GFsxO6A7BFJ7PENafgf5CpNi/9Iltvy8bjrD4yDbOyh3M/LxhvHpkK4esLTw84exouwaEZ9wbS6t45JMNlDW3MzI3gzvPOIUx+d3zAJHpm3xVXsOjn2xkf30zAzJS+NW8U5jULy/abn2Hso42rlv/Js1uO3+bcA5n5XZPv8kj9p0sqXqQLH0R1xTeh0bRtaUhhRDhzALPx+EjLW3kOqnIgtkJkRbMcDX+BaAqCve1lLomeMAbdKNR6KImvsFQ6Duz63qnDaNKQ7w2+l04ylva+euH69h0pJrcpHh+cfpUTh3Sr09MVGSiTygk+HRvKf/8bCP1lg5mDCrk7nnTyEvuOTEJ7R4nt2x6l21ttdw9fGa3BQPtt33FsupH6GcazuX593Z57VkRciHMl4Rrbie9F7FuTrJgdkIkBVOEHOEIL2FDSlreZRFeHze8TIffjFJScWr6QmLU8RHvNtIZ3xQl6Ak4PF6eWv0VSzfvQq9Rc/PsiVw6cQQaVc/NqZPpvXj9AZZs3smzX36NLxjk6qljuGHmeIzanpEm5g0GuLtkJR/WHODSolH8YfTp3fJd3WZexfK6pxgefwoLcm5H0cXl7USgFtF+PigzkJLeRJK6fpIuC2YnREoww9sHd4Dnc6SEV5C0E7pk3F2WdWw1f8HCvHv4vGkpaoWaXMNAhsX37iCiE0GI8Iz/rx+uo83h5IKxQ7n9tCkkmiLf31NGptXu5B+fbmTFjgOkx5m49+yZzB5c1CN2NEJC8MieNTx7aAtzsvrz2MTz0HVD7vO6lvf4vOk1piafwxmZV3f5+MK7HmG5HnTnIcU91OW/azmtpLtxLQHPJ+ED6i4SSwCLr4VcwwAMqhjOylxEkiaTOtcRyh17u8xGb6Km3coNLy/nrmUfkxprZNnNl/LH80+VxVKm20iJMfLAgrm8dtPFxOp13P7aSm5dvIIGS0e0XUMhSdw9Yha/H3Uaq+tLuWrdMjp8nojbnZYyn0lJ89jY9gGbWld2+fiSdhoYbwXPcnC/3eXj/xhkwTxBhH9PuHiwdhYYF3Xp2ANix2L2NdHkrkalUDMsfjJapYEGV3nY9kmyOxAIhnh5/TbmP7aE3TWN/ObsmSy75VKG5XRvz0AZmW8YlZfJ27ct5FfzplFSUcc5/1zM0s07CYWi/528qv84Hps0n93mei5bs4Q2jyOi9iRJYl7mNQyJm8gnja+wz7al622YbgXNFETHnxD+Q10+/vEiC+YJIEJ2hPUOUKQe3So4sV/nfwqgQWkiRZtNqX07zoANoyqOfqYRbLOsxhWw94htoEhT1tzGwmfe4JFPNjCpXy4rf3EVCyeP7HEh/jInHyqlgqtPGcOKO65gdF4mD6xcy5XPvUVVqyXarnFm7mCeP+ViquwWLvlyCQ2uyK6AFZKSBTm3k2Poz9s1j1HjPNyl40uSEinuEVDEIay3I0KRnQR0hvzUOREkA5L+IqT4fyApTiyB99str0IiCEC8JoU840AcARs7LGsAyDUOIEWbhSNgOzHfezjBUIgX123lwsdfp97Swd8umcfjV5xDWlx0u7P3VgKBIC6XF1uHG7PFSXu7A7PZgcXixNbhxuXyEggEo+1mryQrIY5nr5nPgwvmUt7Szvn/WsLijTuivto8Jb2QV2dcRpvHySWrF1PtiKyQqxVaLs//NbHqBF6rfgiLr6VLx5eUSUhxf4dgNaLj/i4d+7h9OFm29SD6DaT/Fw6/lXdq/0WcJpk4dTITkk7HqIolEPIfC9M+Yt/JXutmrP5WJBQIQlxV8DuUUt+MCK01W7n3rc/YWd3AnCH9+P15s0mSzym/g8fjp7nZRktLB61tdtrbHbSbHVitLmw2F3aHB4fDi8vlxe32EwyGjmtcpVKBXq/GYNBiMmmJjdETG6snId5IYpKR5CQTycmxpKXGkpYWi1bbcwuWR4PWDgf3LV/FukOVjCvM5oEFc6Peg3OfuZGr1y1Dq1Tx2syFFMR0fZuub9PqqeOZsl8Tp0nhxqIH0Cq7NrI1ZH8MnE+GOz/pzznh8eQo2U7oSYIZEiH8IS+vVT9EoXEoxTGj2GPdQLXzEDcX/xXgO6IJ4bynkAh2aZTsYWsLTx3cxF/HndUtEXXfhxCCD3Ye5M8rvkSpUPB/58zkrJEDT4qt5/+FEIK2NjsVla1UV7dRU2umrs5Mfb2FdvN/b0mFhc1AbJye2Bg9JqMWo1GLTqdBp1Oj1ihRq5QoFBKKo1vaoVCIUEjgDwTx+QJ4PQHcHh9Opxen00uH3Y3N6sZqddJh/+8AkqQkE9lZCWRnJ5Kbk0ReXjIFBSkkJ5lO6r/b8u37eXDlWpQKBffNn80ZwwdE1afD1hYuX7sUlaRg6czLKYyNrGiW2XfxauWf6R87hoV593RpuokQgXBnk8AhpKQVJ5yfKQtmJ/QkwfxmC/aD+ueYnHwWydpMAF6reggFCi7Lv/vYte3eRpK0GV3uQ6mtlYVrXkOtUPDW7KuOFU+PBg6Pl/vf/5KPdh9ibEEWD150etRn5t2JEIKW1g4OHmzk0OEGSo80UV7egv1bIpUQbyA7J5GszAQyMxJIT48jLS2WlOQYEhNNaDSRzc/1+QK0tztobbPT3GyjqdlGQ4OV+noLtXXt2Gz/LpYdG6unX1Eq/YvTGTgwg0EDM0lJOXn+nhCO6v71m5+yu7aR+WOG8JtzZka1hViprZXL1yxFKUm8PuvyiK80t7R9xIcNLzIj9UJOTb+sS8cWwXpE2zmg6ne0SMxPv/dlweyEniKYK+qfxaCMYVbaxbxV8yj9TCMZl/TvpqlPlP6SsYlzmJh8Bm3eBja1rWRu+uVoFYYum7WXd7Rx6ZevHf3yXEFBTGKXjPtTOFDfzJ2vf0SDtYNbZk/i+hnj+nxQjxCCquo2du+uYc/eWvbuq6O9PbxqVKuVFBakUFycTlFhKgUFKeTlJRMXG/3KSt+H1eqiurqNispWyitaOFLWRGVlK4FAeDs4NSWWIUOyGD48h5HDc8nNTerzq9BAMMSTq7fw/NoSCpITefSyMylO7/rWWMfLN5NkjULJsllXkGuKXMUiIQTL655iu2U1l+bexdD4yV07vvtDhO1OJNMdSKZbfvI4smB2QrQF0xfy8F7tE0iSkvnZN6NR6KhxHmZx1V+4rvB+0vX5ABzs2EqFYy9nZFxNQPhQoOzSslM1DguXfLmYQEiwbNblFMVG5wsshOCtkj08uHIdSSY9D18yr0/XfzVbnGzbVkHJ1kp27qrGYnECkJISw7ChOQwZnMXgQZkUFqaiVveN82mfL0B5RQsHDzawb3/ddyYGSYkmRo3KY9zYAsaNLSQ+vu+eU39VXsPdb3yC0+vjt+fMYv7YIVHz5bC1hcvWvIZRpeGN2VeSaYjcyj8Q8vNCxe9o9tRwU7+HSNN1bXm7kPVO8HwargKkHvaTxpAFsxOiLZgr6p6l3LGHOwc+CUCLp5ZUXQ6bWldSYv6cRYV/JFadyOGO7eyzbeaCnJ91uQ9Nrg4u/nIxDr+P12dezoD46LS8cvv83P/+aj7YeZCp/fN56KLTSTD27BXUj0UIQUVlK5s2lbLl63IOH24Ewluro0fnM3pUHiNH5JGeHtfnV1rfIISgocHKrt017NhZxY6dVdhsbiQJBg3MZOKEfkyZUkx+XnKf+5202p3c8+YnfF1ey4Lxw/jN2TPQqKJT5nKfuZGFa5eSojPyxqwrSNZFLvq8w2/mySN3oVMYuLn4YXTKrpsYiZAN0XYmSDFIye//pPrdsmB2QrQF0xmw8WLFfcxMXUCrt54Kx178IR9jE+ewz7YFoyoWjUJLpfMAk5PPZELS6V1q3+x1cemXS2hydbBk5kKGJ2Z26fjHS73Fxs+XrORwUyu3zJrITbMmolD0jYejEIKy8mbWrjvEuvWHaGiwHhODCROKmDihiKLCtD7zeU+UUEhw5EgTX5WU89W3JhXZ2YlMnzaQmTMGUljQd/qYBkMhHv9iM8+v3crQ7DQeu/xs0uNiouLLttZarl63jPyYBF6feQWxmq7tOPJtKh37eaniPgbFjufSvF916WQoXDrvOjBehyLm7h9+w38gC2YnRFswAaqdh3i54o/0ixnBZXm/os5VxqGOraTqckjX5dPsqSFWnUiBqWu3bJx+H1esXcpBazOvTL+UCanRaVNUUlHLL5Z+SDAkePjiM5g2sCAqfnQ1TU1Wvli9n9WrD1BT245CITF6VD7TThnA5En9SEyU80ePh7Y2O5u3lLF+wyF27a4hFBIU5Kcwe9Zg5sweQmpq3wgcWrW/jHvf+hS9Rs1jl5/NqLzoTF7XN5Zzw8a3GJmUxSvTLo1opPyG1vf5tHEx8zKuYUpK17YGDNl+C+53kBLfQNKM/FHvlQWzE3qCYALUuo6Qos1Ed7Tx6obW93EFHMzNuDwi9vyhINdveItNzZU8NeUCTs2KToj7WyV7+MuKNeQmxfP4FeeQn9JzWiT9FLxePxs2lvLxJ7vZtbsGgOHDcpgzewinTO1PXFzfPZPrDiwWJ+s3Hmb16gPs21+HJMHoUfnMO2MEUyYXRzwqONKUNbdx2+IPaLI5+MP82Zw3Jjrnmh/WHOCOLcuZk9WfJydfELGAOyEES6v/yuGO7dzQ7y/kGPp33dghx9GtWcOP3pqVBbMTeopgfhtP0Mmy6r8zMHYsk5Lndfn4QgjuKfmQd6v28OC4M7mo8MfNvrqCYCjE3z5ez5JNO5naP59HLp1HjK5reoVGg9o6Mys/3Mlnn+/FbveQkRHP6XOHceqcoaSnxUXbvT5JQ6OVL1bt49PP9tDc3EFsrJ4zTh/OWWeOJCuz9068rC4Pd77+IV+X13L9jHH8/NQpUdmuf7V0K/fv/JyFRaP545jTI3Z+7A46ebL0lwgEt/V/FP3RRUNXILwbEJZFYLwFRcwdx/0+WTA74ccI5rdL1UWCkAhS5yrj3drHGZkwg5lpF0bEzmP71vOv/Ru4fcgp/HzotIjY+D5cPj/3vPkJXx4o5/LJI/nVvOmolL0vZUQIwdZtlby3fBslWytQKhWcMrU/Z505kpEj8uQzyW4iFBJs31HFhx/tZNPmIwghmDChiAvnj2PUqLxeGSjkDwb584oveWfrPk4f1p8HFsxFq+7+1fNDu1fz/KGvuHv4LG4cNClidmpdpTxX9n8MjhvPJbl3denfLGS9GzwfhhtOqwce13tkweyEHxJM4T8AwWbQjAVJFZFmpd+m1VOH1d9KccyoiIz/XuUeflWykgvyh/PX8Wd1+8Ok3eHillff50B9C78+azoLJ0fmc0YSvz/IqtX7efvdEqqq2khMNHLu2aM5c94I+VwyyrS22fnww52s/GgXVquLosJUFlw4nlkzB6HqZY3EhRC8vGE7f/9kA6PzM3n8inOJN0QuCOd/ERKCO7a8z0e1B3hi8vmckTMoYrbWtyzns6YlnJd183dy0E8UEbIg2s4AZTZS4ptIx1E+VBbMTvg+wRSeLxD2h0A9FEI2JO0poBn/k3N7ok1JSw1XrlvK2ORcXpp2CRpl9z5Aas1WbnhpOS0dDv52yTxmDS7qVvsnisfj56OPd/Hm2yW0tdkpLEzhogvHM3PG4D6TI9lX8PkCrP5yP2+9s5Xq6jbS0mK55KKJnHH68F53zvnpnsP8+q3PyEmK47lrzicjvnsjaL3BAJevWcp+axPLZl7OiKTI5EWHRIhXKu+nxnmYW4sfIUXXdXaE+wOE7S6kmN8hGa/4wetlweyEzgRTCD/C9lsk/Xwk7USEdzPC9zUQQtJOR9Ic1++yx1DjsHD+Fy+ToDXwzpyriNN0b37j4cZWbnj5PfyBEE9edW7UIgB/Cl6vnw9W7uSNt77GYnEyfFgOl106iXFjC3rldt/JRCgk+LqknKXLtnDgQD1JSSYuvWQiZ80b2auEs6Silp8t/gCTTsNz155PUWpkS9j9J+0eJxesegVP0M/yU68lI0KFDTr8Zv5VegeJmjRu7PcgyhMob/dthBAIyzXg342U/CmSMu17r5cFsxM6F0yB6PgdSDoUsb8NvxaoAM/HCBFCEfPz7nb1J+Pwe7lw1au0eOy8O+eabi95t7umkZteXo5eo+a5a8+nX1r3ftl/KoFAkI8+2c1rr22m3exg9Kg8rrh8CiOGd21lEpnII4Rg565qFi/ZxJ69taSmxHLF5VM4fe4wlL3k/PxgQws3vryckBA8d818Bmd9/0O/qym1tbJg1SvkmRJ4c/ZV6COUbrLPupllNY8wM3UBc9Iv7bJxRaA6HDWrOxVF/D++91pZMDvhe7dkg/UIxzNImjGgOxNJUiMCtQjrTUimXyLpZnWztz+ekBDcsukdvmw4wsvTLmVKevfmOH5dXsuti1eQEmPkxUUXkJnQ83PmhBCsW3+YF19aR32DhWHDsrn26mmyUPYBhBDs2FnNSy+v5+ChBnJzkrhu0XSmTC7uFbsF1W1WrnvxXTrcHp65Zn6379SsaTjC9Rve4qzcIfxj4rkR+529XfMYe6wbuLHfg2Qbirts3JD9X+B8AinhVSRt50FMsmB2wvcKpvCA+yNE4DCSKg+0pyIpUwl1PISk6o9kOL+bvf3xPL5/A//ct57fjjyVawaM71bbm0qr+dmSFeQkxfPCogtIiem6cPFIcfBQA089vZr9B+opLEjhukUzmDC+sFc8TGWOHyEEmzYf4YUX11FT286I4TnccvNsivulR9u1H6TRamfRC+/QYnfy9FXnMa4wu1vtP3VgE3/fu5bfjJzDogETImLDHXTyeOkdaBR6bi1+BLVC0yXjCuFBtM0DtEjJHyBJ/3uVLAtmJ3wjmN9OGfnm80uShBBe8HyBCBwE7xbQTADPinDPNWVKNF3/QdY2lnHd+jc5N28oj0w4p1sf+hsOV/Hz1z6gMCWRFxZd0ONrwprNDp5/YS2ffbGPhAQji66ZxtzTes92ncxPIxgM8dHHu3n51fV0dLiZd8YIFl0zvccXfW+1O7n2hXdosHTw5FXnMrGo+3Y/hBDctvk9vqg/zKvTL2NSWn5E7Byx7+KVyvs5JeU8Ts+4ssvGFZ7VCOvNSDH3Ihmv+Z/XyILZCccEM1ALijgQfiRl+IxNiMCxnmoiZAP/HghZQT0USdWzy7fVOa2c8/mLZBpieXv21RE7b/hfbCyt4mdLPqAoNYkXFl3Q7aHwP4ZgMMQHK3fy0svr8fkDXHD+OC6/bBIGQ+8toiDz43E4PCx5bRPvvb8dg0HD9YtmMO+MET06l7bd4eLaF96hzmzj6avPY3xhTrfZdvi9XLDqFSxeNyvnLiJNH5nI3eV1T7Hd/CU39XuIbEO/LhkzHAB0Hfh3IaV8gaT475gOWTA7YezYsWLr5qcRHX8A9UgI1iLpFyDpw3UNhfAiSVqECCF1YYfwSOINBrh49WKqHGZWnLaIvAj2t/tPviqv4ZZX3qcgJZEXr7vw/9k77/CqqqwPv/u23PReCaSH0HvvRZoCn45ir+PYFXt3HB17RRwdrKBi7w0FpEhHOqEnkN57z63n++MmDGKEBM4592LO+zw8xuRm7ZXk3PM7a+9VPFosMzKLefGlnzmUUczgQQncdstZxMa6bwaohvvJziln/qvL2Lkrl549YrjrjukkJHjuTlJFfSNXv/U5hdV1vHn1uQxUcRReZm055y5/l55BUSyecClGnfylVc2OBuYdnIuPwZ+bkp+TbaShZM90DZv2Ph9d4ON/+HpHBPPMUAWZ8PGWkGqfRvjdgQh4BOF7PVLdMzjr5gEcFUupfr6rAPYMeJh4dtdK0quKeHboOaqK5Y6cQm5571u6tZxZeqpYWq123n7nV268+T3Kyut45KHZPPv0HE0sNYiPC+PF5y/m/nvPoaCwiutvWsii99Zisznc7VqbhPr58M615xMZ4MeNi75hb0GJamsnB4Tx5OAZbC3PY96eNYqsYdb7Mjv2ekqac1hb9q1sdoUhGXwuhabPkGwHT8tWpxLMxibh6uKjj0IIM8JrFCL0K7CswFn7lOtFUh3CNBChCz6tc8AGey1OySmT522zLP8g72Vs4aqUIUyNbV8bKDk4UFTGjYu+ISLAz6PPLPcfKOS6Gxby0ScbmTqlD4ve+QcTxvfQkno0jiKEYB7FdmYAACAASURBVMpZvVn0zj8YP64H7y9ez403LyIjs9jdrrVJuL8v71z7NwJ9zFz37ldkllSotvasuN5cmNifBfs38GvRYUXW6BEwhN6BI1ld+jnllkLZ7Aq/m0H4I9U9e1p2PFYwhRDZQoh0IcROIcQfUluFi/lCiEwhxG4hxMCT2ewa4wBhQmpY9D87+khE8FvgLEey5yF0gQiv0+u56pScLM5+mo9ynjstOyeisLGW+7f8QO/gKO7rN0mxdY4np7ya6979Cl8vE29f+zfCPDAb1m53sHDRGm6d+wHNzTaeffpC7rlrBv7+nhkFa7ifwEAfHrx/Jk88/jdqapq46Zb3WfzhBhwOZR96T4WoQH/euuZvGPQ6rl/4FYXVtaqt/ciAKaQGhnPP5u8pa6pXZI2zY67BIIx8V/CmbLt8QheE8LsJrOuQLOtO2Y7HCmYLEyRJ6v8n+8vTgZSWf9cB/z2ZsbxCPcLvTpAacFZc4sqKBYQ+CiQ7OI7I4vS2yhXkNh6kZ4AypR0Op5O7N32Lzelg3ohzVWt7V17XwPULv8LhdPLWNecRE+R5dZYFBVXcevtiPvhwA5Mn9eLtt65hyGDPTtrS8BxGjkjhnbf+ztgx3Xl30Rpuv/NDiour3e3WH4gLC+KNq8+jwWLj+ne/prqhSZV1vQ1GXhlxLvV2C/f+9j1OBY6tAowhnBV1KYfrd7O7eq18hn0uBX0sUt1zSKe4++fpgnkiZgPvSy42AUFCiOiTfpfjCML/IZBqkCqvcfUdbHgH7AfBcPrz2RrtdSwrXky8b08GBE84bXtt8dbBTWwuy+XRgVNV6+TTYLFy03vfUN5SD5YY4XlngMt/2cN1Ny6ksLCKRx/5P+6/9xz8fLWoUqNjBAR488hDs3nogZlkZ5fzjxsW8uuaA+526w+kRYfznytmkV9Vw80ffEuzza7KuqmB4TzYbxJrio/wQYYy4xKHhk6hi3cSS4oW0exolMWmECZXwGQ/AM0/npINTxZMCVgmhNgmhLiuja93AfKO+f/8ls/9KZPH2JCq70VqeAOMgwALOMuQHHmIwCcR+pPr7clYXvwRzY4GZsb8Q5Gzsr1Vxbyc/ivTY9P4W3xf2e23hd3h5O6Pl3CgqIwXLzmbvt1O//ckJxaLjedfXMLTz/5AcnIEby24hnFj1TvT1fhrMmliL95ccDXduoby2L+/Yd78pVit6ohSexmcEMszc6axK7eI+z79CadTnUTFS5MHMSE6mWd2rSCjpkx2+zqhZ2aX62iw17Cy5FP5DJtngKEHUv3LSJK1437J54nsjJIkaSCurdebhRDHHyy2pUZ/uFqEENcJIbYKIbYO7FWPCH4d4X8fwjwNjIPB50p0Af+SpcF6YdMRtlQuY3jYdKK8407b3vFYHHbu3vwdIV4+/HvwdFWSVyRJ4pkfVrPmYBYPz5rIuLRExdfsCAWFVdxy2wf8vHQ3l14ykpeev4SICM/bKtY4M4mODuKVly9lzgVD+e77Hcy9YzHFJTXudut3TO2Tyj0zxvHL3kxeXnrq53MdQQjBM0PPxs/oxd2bv8PmlD+zuKtPCoNCJrGxfAmlzXkn/4Z2IIQO4X8nOPKh6YsOf7/HCqYkSYUt/y0FvgaOPxDMB46t3o0F/pBWJUnSm5IkDZYkafDQgUZAj9D5gTEN7HvBkS/LwbIkSfxQ8A4+en8mRl502vba4pU9azhUU8ZTQ84m2Eud7iQfbdzFx5t2cfWYQcwZpk5E2142/3aYG25aRGlZLU89cQF/v3qs1q1HQ3YMBj03XDeRx/91Hvn5Vdxw0yK278h2t1u/44pRA7hwWF/eXbOVL7fsUWXNMLMfjw+axp6qYhbs36DIGlOiLsWkN/Nj4bvylfmZxoJxEFL9666WqB3AI+8uQghfIYR/68fAFOD4q+A74IqWbNnhQI0kSUUnsltQJJCqb0Sy7UGqfQb08QhDvCyR2p6ajeQ07mdy1CV46+XPHN1ZUcBbBzcxJ6EfE2Lk6YJxMjZm5vDsj6uZ0CORO6aNVmXN9iBJEp98uokHH/6c6KhAFrx2FcOGnlnzNjXOPEaPSuW/r11JcLAv997/KV99vdVjarWFEDw4cwIjU+J4/NsVbMsuUGXd6V17MLNbL/6zdx0HquWvC/U1BDIp8kIy63dxsG6bLDaFEAi/28FZCo0d2+71SMEEIoF1QohdwG/Aj5Ik/SyEuEEIcUPLa5YAR4BM4C3gppMZnfuoL8I8C6l5Begj0AX+WxZnbU4rS4veJ8ocx+AQ+Us8LA479//2AxFmPx7sP1l2+22RW1HNnR/9SGJ4CM9eOB29zjMuFavVzjPP/cCbb69m3Ng0Xnn5MqKjg9ztlkYnITY2hNfmX86I4cn85/VfePmVpdjtntHowKDX8cLFM4gNDuT2xd+rVm7y6MApBJq8ufe3H7A75S/DGRY6jTBTDD8VvYdDkucMWXgNA9NwVz5LB/CMu+BxSJJ0RJKkfi3/ekmS9GTL5xdIkrSg5WNJkqSbJUlKkiSpjyRJ7UrXEr5XoPOfi87/btn83VS+hCpbKTOir0Yn5C/xWLB/Axm15TwxeDr+JuWzPhssVm774DsEglevmIWvlzzTA06Xmtom7rn/E5b/sperrxzDIw/NxtvbM3zT6Dz4+Hjx2KPncclFI/jhx5088NDn1Nd3bGtPKQK9zfznillY7Q5uX/y9KpmzwV4+PDZoKnurinn30GbZ7euFgWkxV1JuKWBLxXLZ7Aq/W8FZ3qHv8UjBPJNotNexuvQLUv0HkuQv/xlfRk0Z/92/nlndejEhRr5ZcX+GJEk8+tUvHC6t5IWLZ9A1xDOit6Kiam6d+wEHDhTx8IOzuPyyUVrHHg23odMJrv37OO65awY7d+Vy2x2LKStTr4HAiUgID+HpOdPYW1DKE9+uVGXNabFpnNUllXl71pBTXyW7/TT/wST69mZFyafylZmYhrgmUnUATTBPk19Lv8TibGZa9OWy23ZKEg9v/QlfgxcPDThLdvtt8eGGnfy0+yC3TRnJyBT5M31PhczMEm69/QNqahp54bmLmDihp7td0tAAYPq0vjz71BxKS2u5Ze4HZOd0LGJRiok9k7h+wjC+3raXL7akK76eEIJ/DZyKUeh4dNvPsp/tCiGYGn0FjY5a1snZZzZofoderwnmaVBtLWNTxU8MCB5HpFl+cfkyaxdby/O4v99EwszKt6DbnVfM8z+tYXyPRP4+doji67WHXbtzueOujzDo9cx/+TL69FZvrJGGRnsYODCeV166FIfDye13LGb/fvl6oJ4ON08ezsjkbjz53SoOFMlfK3k8UT4B3NlnPGuLj/BD3j7Z7cf6JNMncCTryr6j3iZP9yWh69jACk0wT4OVJZ8hITFJgTKSKksjz+5ayeCwrvwtoZ/s9o+ntqmZuz/+kQh/P548f6pHzAb8bcsR7nvgM0JD/Zg/7zLi4sLc7ZKGRpskJUXy6rzL8fUzc9e9H3tE2Ylep+OZC6cT6G3mro9+pMHS8UL9jnJZ8iB6B0fx1I5fqLNZZLc/OeoSHJKN1aUdr6GUA4NbVv0LUG4pZEfVKoaFTifIJP8MvZfSf6XW1szjg6ahU/isrvXcsqSmng+un+MRo7rWbzjEY//+hvj4cJ57+kKCgtSpOz2TkSSJ+uoGyvMrKC+sorq0htryOuqq6mmsbaKpvhmbxYbNasfpcCIECJ0Oo8mA0cuIt58ZnwBvAkL8CQjzJygikNCYYMJjQ/EL8rwm+55GdHQQ81++jHvu/4QHH/6Cx/91HkOHuLfRR6ifD89fNINr3v6CJ75dydNzpim6nl6n49+DpnPeLwt5dc9aHhwgb1Z/mFcMA0Mm8VvlMkaHz1bk3nsiNME8RVaVfI5eGBkXcZ7stvdWFfPx4e1ckTKE7kERsts/nq+27mXZngzunDbaI9rerVl7kH8/+S2pKVE8+/Qc/PzcL+CehMPuIPdAAVnpueTuyyf3YAEFGUUUHymlse6PTbiFEHj7mzH7mvHyNmEwGY42eHA4nNitdixNVpobmmmqa27z/MknwJuYpChikqPo2j2GuJ5dSezbjdjuMehVav5/JhAa6sfLL1zCPfd9wiOPfsljj57H8GHurREekhjLDROH8fqKTYxKjeec/sq2jewbGsMFCf14L2MLc5L6kxwg787QhIjz2VG1itWlX/B/sTfKavtkCE8pvFWDwYMHS1u3nn6z4LLmfF45dDujw2cxLfoKGTz7H5IkcdHKDzhSV8GKGTcSoHAZSU55FX+bv5i+3aJ5+5q/uX0rdt16V2TZvXs0zz41B19fL7f64wlUFFWxZ90B9q4/wMEtmWTuyMLabANAp9cRkxRJl5RoohMjiYwLJ7xrGKExwQRHBhIYFoBPgDe6dtbROp1OGmoaqSmvo7qkmorCKkrzKijJLqUoq4T8Q0UUHyk52rPUy9tE8sAE0oYk02tUGr1HpxEc6RmZ1e6krq6Ze+77hKzsMp547G8McXOkaXc4ueqtz8koLufruZcTE6xs+8iK5gYmL1lAv9AYFo69SPaM9u8K3mJLxTLuTHuNYNPpBRVCiG1/MhHrj6/VBLPjfJY7j301m7mnxwJ8DYEyePY/luTt59YNX/HE4OlcnHTSEZ+nhd3h5PI3PiW7vIpv5l5BZKCfouudjE2bD/PPf31JSnIUzz1zYacVy8a6JnasSGfbsl3sWJlO/iFXAysvbxMpgxLpPjiJ5IGJJPWLo0tqDCYvo6r+WZut5B0s5MiuHDK2H+Hg1sNkbj9yVMS79ehC/wm9GTy1P/0n9sa7k06Mqa1t4u77PiEnp5ynn7iAgQPj3epPfmUN581fTM+YCN699nzFH44XHvyNJ3Yu5+0xc2QviauxlvPiwZsYGDzhtKNMTTD/BDkEs8JSxMsHb2VU2DlMj7lKHsdasDjsTPlpAb4GL76f8nfFu+u8ueo3Xlm2nucvmsGMft0VXetk7NqVy30PfkZcXCgvPndxp9uGrSiqYsM3v7H+2y3sWrUHu82Bt5+ZvuN60m98b/qMSSN5QAIGo2eeotisNjK2Z5G+Zj+7ft1L+pp9NDdYMJoM9J/Uh5GzhjDq3KEER8j7gOnp1NQ2ceddH1FUXM0Lz15Ez54nHKikOF9v3cvDXy7jvrPHccVoZR/IrQ4HM5a+iQ7BkmnXYZD5fvZtwRtsq1zBnd1fJ8h06tu+mmD+CXII5ld5r7Greg13py3A39ixlOST8faBTTy9awXvjbuY0VHKbuEcLCpjzmsfMblnMi9ecraia52MQxnF3Hn3R4SH+TPvpUsJDOwcCT61lXWs+XwTKz9ey561B5AkidjUaEbMHMywswfRc2QqRpO60aNcWC029q4/wOYftrHx+60UHi5BpxP0HdeTCRePYdwFw/EN7ByJRBUV9cy9czG1tU288tJlJCSom6hyLJIkcfP737IpM5cvb7uMhHBl59ouLzjIDeu+4PFB07g0eZCstquspbx04GaGhU7lnC7XnrIdTTD/hNMVzNZtgMEhZzGryz9k9AxqrE2M/+F1+oXGsGjcxbLaPh67w8nFr39MSW09395+BcG+3oqudyIKCqu4be4HGE0GXn3lcsLD/N3mixo4nU52rEjn53dXsv7r37BZ7XTr0YXxc0Yx9oLhxPX869WZSpJE9p5cfv18I6s/3UBBRhEms5HR5w1j+t8n0W98r79816bi4mpunbsYoRP855XL3TqCrqy2nlnz3icpIpT3r5uj6NasJElcsmoxh2srWHX2Tfga5W1l+WXef9hdvY57eizAz3BqZ+cdEUytDrMDrC//HklyMiZ8tuy239i/kTpbM/f1nSi77eN5b9029hWW8tCsCW4Vy+rqRu5/4DMcDifPPXPhX1os66sb+PzF77m6+23cP/UJti3bxdnXncVrW57h7T0vc/mjF/wlxRJcWboJfeK46vGLWHjgFV7d9BRTr5rA5h+3c8+kx/h7z9v56pUf28zw/asQFRXEM0/PoanRyn0PfubW3rPhAX7cd/Y4duQU8vGmXYquJYTg3r4TqbA0KNJndmz4uTgkGxvLl8huuy00wWwnTY4GtlQup0/Q6NPOyjqe0qY63svYwuy43vQIjpTV9vHkVlTz2i8bmdQziSm9le9N+2dYrXYeefRLysrrePKJC+jWNdRtvqjBU5fM48173ic4KogHFt/GJwVvcvP8a0gdlPSXj66ORQhB2tAUbnv9H3xa+Cb3LroF3yBf/nvHIi7uej1v3vM+5QUV7nZTEZISI/j34+dRUFDJo499jc3mviknswf2ZGRKHPOWrqOouk7RtQaEdWFKl+68fWATVRZ5+sC2Em7uQo+AoWyu+BmLQ/kHLk0w28mWiqVYnc2MViC6fH3feuxOJ3N7j5Xd9rFIksS/v1mBQa/noVkT3XajliSJ515Ywt59BTxw3zn0cnMihBpc+diFvL71WeatfYKJl4zBZNamrHh5e3HWFeN4deNTvLrpKYZOH8CX837k8sSbeekfCyjKkn++orvp3y+Ou++czo6dOcybv9Rt8zSFEDz6f5NwShJPfb9K8fXu7DOOBruVNw5slN32mPD/o8lRz7Yq5RvNa4LZDuxOGxvKl5Dk15cY7wRZbRc21PDJkR2cn9CPbn7yJhEdz8/ph9iQmcvcKaPcWkLy0ccbWblqH9f+fRzjxipbRO0pdB+STMpA99bieTJpQ1N46OM7WHRoPtOvncwvi9dwdfe5zLv+Dcry/1oR55Sz+nDZpSP56efdfPn16Ze5nSqxIYHcNGk4K/cdZuW+w4qulRIYzuy43nyQsZXy5npZbXfz7U43n+5sLP8Bp6Rs1K4JZjvYU7OBOnslo8Jmym779f3rAbi55yjZbR9LfbOFZ3/4lV5dIrhouPxjyNrLho0ZvLNwDZMm9uTiC4e7zQ8NzyQ6IZLbXruW9zNf5ezrJrN00SquSr2Vt+79gIaaBne7JxtXXTGG0aNSWfDGSrZuy3KbH1eMHkhSRAhPf7+aJqtN0bVu6TUaq9PBm/s3yW57VNhMKq0l7K/dIrvtY9EEsx1sLF9CmCmGFP8BstotbKzli6xdXJDQnxhfZevTFqzaTFldAw/PnqR4feefkZdfydPP/EBqShR33zn9jDy7O7I75y+5VehphHUJ5db/XMvCg/MZe8EIPn/xe65KvY0f31yOw+G+sz+50OkED9x3DvFxYTzx5LcUF8szfaOjGPV6Hpk9icLqWt5do2y0m+Afyuy43nx4eBvlzfI+/PQIHEaQMYxNCif/aIJ5EvIaD5HflMHwsBnohLy/rjf3b0CS4IYeI2W1ezzZZVV8sH4H5w3uRd+uUYqu9Wc0NVl59LGvMBh1PPavc/FSuTvN6dJQ08DDM5/m6Utf4fmrX+PnhauwWlxP5J2pNEttouIjuO+9W3ltyzN0TevCvBve5NbhD3Jwq7JbiGrg7W3isUfPw+GUePTxr7Fa7W7xY0hiLNP7duedX7dQWKXsEOybeozC6nTw9kF5o0y90DMsdBpHGvZQ3JQjq+1j0QTzJGyu+BmTzsyA4PGy2i1vruezrF2cG9+HLgpHl88t+RUvg4G5U5Td9v0zJEli3vyl5OSU8/CDs4k8A7u9HNx6BN9AH95Kf4lrnriY9LX7WPXxOoAzMlI+00gZmMiLqx/jgQ/nUlFYxW3DH+C/dyyiqf7MLkXp0iWYB+47h4yMEl57/Re3+XHX9DEIIXjp57WKrpMYEMqMrj34KHM7NVZ5/3aDQ87CIIxsrvhZVrvHognmCWiw15JevZ4BweMx6+XtPrPo0BasDjvXpY2Q1e7xbMzM4dcDWVw/YShh/u7prPLz0nSW/7KXKy4fzSA399M8VQxGPSU5riG8vUf3oO/YnmTvyTsa6WhRpvIIIZh48Wje3T+Ps6+fwtfzl/CPPnexc9Ued7t2WowckcJFc4bx/Y87WblK/sHL7SE6yJ9rxg7mp92H2J5doOhaN6SNpMFu5YOMbbLa9TH40ydoNDurf6XZIW/5SiuaYJ6AHVWrsEs2hoVOldVuvc3Ch5nbmRqbRmKAcvWHTqfEC0vWEhMUwGUj5T1/bS+5uRW8+tpy+vfvxmWXKLv1LAd2W9vbYt5+ZlIHJbF7jeuGNmBib/QGHVnpuUiSpEWZKuIb4MNtr13LS2sex2AycM+kx3j99oVYm5UfkKwU11w9ll49u/DyvKUUFbnnPPPqsYMJ9/flxZ/WKvoA2CM4knHRSbyfsZVmu7yJRsNCp2F1NrOreo2sdlvRBPNPkCSJLRXL6ebTnUhznKy2Pzuyk1pbM9crHF3+uOsAB4rKmDt1FF5uaNptszl44qlvMZkMPHjfzKMzGD0Rh8PBon9+wkPnPM26rzdTXljp+rzdlWASGhOMb6APB3/LxGqxEdEtHG9/bwoOFSKEwOl0utP9TknvUWn8d/tzzL55Gl/PX8LNQ+8ne2+eu906JQwGPQ89MBMEPPn0dzgc6l9PPiYjN08ewc7cIlYoXGZyXdoIKiwNfJWdLqvdWO9kos0JbKlYrojoe+4dzM3kNO6n3FrIkJCzZLVrdzpZeOg3hoR3pW9ojKy2j8Vqd/Dq8g30iIlgRl/3TCJ57/11ZB4u5Z67phPm4W3v3vvnp2TvyeW8uWezZ90BXr99IQB6g2s4ckhUMCmDEikvqGTN567i654jUik84sqYbe+8SQ158fY1c8urf+fJHx+kurSWW4bez7L3VrvbrVMiKiqIO+ZOZd/+Qj7+RP7Si/Zw7qBeJIaH8MrS9dgVFO1h4d3oHRzFwkO/4ZRR2IQQDA6ZTFFzFoVNR2Sz24r2Lv8TtlauwEvnTe8gebcRlxccpLCxlqtTh8pq93i+3LKHgqpa5k4Z5Zah0Hv25vPJZ5uYMa0vo0amqr5+e2iNIpsbLTjsTs6dezbDZgzk+heuIDs9lzVfuITR1lKfNmBSHwZP7cd7j37KB499zkvX/pdhM5QdkaTRPoZOH8CCHc+TNiyF569+jZf+seBoFvOZxMQJPZk4oSfvfbCOQxnFqq9v0Ou4bcpIjpRV8v3O/YqtI4TgmtRhHKmr4NcieaPZfsFjMQgTW6vkT6LSBLMNLI4m9lRvoG/QaEw6eecyvpexhVjfQCbHKCcizTY7b67ezMD4GEanyrud3B4sFhvPvbCEiIgAbrpxkurrn4zNS7ZzZeqtPDLzGQDMPl7kHsinLM/VUUYIwWX/vIBF//wU4OiILW9fM0OmDeC+927BN8iHuxfezJQrx7vlZ9D4I6HRwTy7/BEufuBcfnpnBXdPePToQ9GZxNxbpxAU6MNzz//oln6zk3sl0zMmggUrNmFTsOZ1etceRJj9eD9D3mYD3npfegUOZ3f1OmxOec+1NcFsgz01G7BJFgYGyzs5ZH9VCVvK8rg8ebCizQO++C2d0toGbpk80i3JKIveX0d+fiV33zEdHx8v1dc/GQc2Z3DBXbOIjA/nm//8BMD4OaP48Ikvjr5m4sWj8QvyYdMPrky+/EOFfDXvR8CVJXve3LPpN66X+s5rnBC9Xs81T17CI5/dSVZ6LrcOe4DMne7rpHMq+PubufOOaRzJKuPDjzeovr4QglvOGkF+VS3fblcua9ek13NJ8kDWFB8hq07e9oeDgifS7Ghgf+1vstrVBLMNdlT9Sqgpmq4+8kaBizO3YdYbuCCxn6x2j8Vis/POmi0MTujCsCT1x0Udyijm8y9+4+wZ/RjooSUkF973f5xz/VlMv2Yiyxatwul0MunSMRiMBpa8veLo6/qN730089LhcJI6WOsFe6Yw9vwRzFv3BEII7hjzCJuXbHe3Sx1ixPBkJk3syUcfbyQru0z19cd2T6BXl0jeWvWbolHmRYkDMOp0fJgp798nwa83gcZQdlStltWuJpjHUW0tJ6thD/2Dx8kandXZLHybs4eZ3XoRaFJuBuXX2/ZSWtvAjZPU79PqcDh58eWfCAry4fp/TFB9/fZibol6h0wfQGR8BJ888w0A1z1/OUsXrmT9N79xeFc2u1bvITrRNW4trkcsvUf3cJvPGh0nqV888zc9RWxqDP+c/ewZlwx0842T8fHx4qWXf8bpVLfOVwjBTZOGk19Vy487Dyi2Tri3H1Nj0/gyazdNMpaY6ISOfkFjyazbSb1dvjIdTTCPI73a1b2lX5C8o7a+z9lDk8PGJUnKJYnYHU4WrtlKv67RDEtUP7r89vvtZGSUcMtNk/Hzk/fsVwl0Oh2zb57G6k9dDfCHTBvAubfNYM+6Azx96SuMnzNKmzByhhMWE8KLqx+j3/hePH/1a3zx0vfudqndBAX5cMN1E9i7r4Cly3arvv64tARSo8J4Z81WRQX74qSB1Nqa+SlP3iSjfkFjceJkT7V8I8U0wTyOXdVr6eqTQqiXvD1XPzmykx5BEfQJiZbV7rEsTT9EflUt144fovrZZWVVAwsXrmXwoIQzZmSX0+mk/4Te9BnTg/k3v81nz39LSHQw1z57KW/ufpHzbj/b3S5qyICPvzdP/PAAY84fzht3v8+HT3zpbpfazZSz+tCndyxvvLWa2lp12wAKIbh23BCOlFay+oD8JRqtDAvvRoJ/CJ8c2SGr3SjvOCLN3WRtYqAJ5jGUWwopas6ib9AYWe3urSpmb1UxFyYOUEzIJEni3TVbSQwPYXya+lHRW2+vxmK1cestZ50xXW90Oh0Ou4Oq0hp+evsXio6UkDY0Gb1er9VV/sUweRl56KPbmXz5WBb98xPe/9dn7napXeh0gttunUJ9fTMLFynb57UtpvZJpUtwgKKTTIQQXJDQn23l+RyuLZfVdt+g0eQ2HqTaKs85sHZXOIb0atfWXK9AeTvwfJG1C5NOz6w45bIqNx/J40BRGVeOGah63eXBg0UsXZbO+ecNoWtsiKprny5LF63GL9CXj3IXMPe/12Eym9ztkoZC6A167n73JqZeNYEPHv+cj5/+2t0u5p5Q+wAAIABJREFUtYukxAhmnjOA73/coXoCkEGv44pRA9mRU8iu3CLF1jkvvg96IfgiS96t5z6BowFX5YMcaIJ5DHtqNhLnk0agUb7+rlaHg+9z9jK5S6qiyT4frN9BiK83M/urm5giSRKvv7GCoCAfLj0DesUez7RrJnDnWzcQHBnkblc0VECv13PHW9cz8ZLRvPvQR3w9X9n5iXJx1ZVj8PExseCNlaqvfe7gXvibvfhgvXKZxuHefoyLTuLbnHQcMraZDPWKItqcwN4aeTonaYLZQoWlmOLmbNmjyzXFh6myNnFefB9Z7R5LbkU1vx44wpxhfVXvGbt+Qwbp6flcdcUYfH09r+byZGhbr50PvV7PvYtuYdS5Q3n99oWsbBnT5skEBnhz+aWj2LI1iy1b1a0r9fUycd7gXizfk0lJTb1i65wb35eSpno2lco7z7JX4HByGw9Sazv9Jhba3aKFfbWuJ5CegcNktfttzh5CvHwYHaXcueKnm3ejFzouHNZXsTXawuFw8vY7v9Ktayhnz1CutlRDQ270Bj0PfjiXvuN68vxV/2H7L+pnoXaU2bMGEhUVyFtvr1K9zOTiEf1wSE4++02539OkmBT8jF58kyPvuLZega4Su301m0/bliaYLeyv2UK0OYFgU4RsNutsFlYUZnB21x4YdXrZ7B5Ls83OV1v3MKlXEhEBfoqs8Wcs/2UPuXkVXHP1WI+eRKKh0RYms4nHvr6XrmldePyCF8nZn+9ul06IyWTg6ivHkHm4lDVrD6q6dteQIMamJvDFlnTFGhl46Q1Mj01jWf4BWcd+hXvFEmqKZn/t6bfg0+5yQIO9htzGg/QIGCKr3V8KDmFx2JkZ11tWu8eyNP0QtU0W5qgcXdpsDt5fvJ7UlCjGjPbM5uoaGifDL8iXJ76/H5PZyMPnPE11WY27XTohEyf0JC4ujEXvrVV9BNicYX0pr2tkpYKjv2Z260W93cpqGRuyCyHoETCUrIY9pz1YWhNM4FDddiScpMksmEvy9hHtE8CA0C6y2j2WL7akExcapHqjgqXL0ykuruGqK8ecMWUkGhptEdEtnMe/vY+KwiqevHje0Rmonoher+PqK0eTm1fBqtXKTRNpizHd44kK9OfLLfJumR7LsIg4Qrx8WCJzE4O0gME4JDuZ9btOy44mmMDB2m34GYKI9k6QzWadzcK64iymx6ahU0hQssoq2Z5dyHlDeqsqWna7g48+3khaWjTDhmqdcDTOfNKGpjD3v/9g58o9vH3/h+5254SMHtWdxIRwFn+4QdUoU6/Tce6gnmzIzKGwqlaRNQw6HVNju7OqKEPWbdluvmmY9b4crN12WnY8TjCFEF2FEKuEEPuFEHuFEHPbeM14IUSNEGJny79/nup6DslBZv1uUv0HohPy/TpWFWZidTqYGqtc15tvtu1DrxPMHqBuKcnKVfspLq7hskvcMw1FQ0MJpl41gZk3TuWLl75n/TfyTrmQE51OcOklI8nNq2D9hkOqrn3u4F5IEny3Q7nodnpsDxrtNtaWyNddSC/0pPj1d+0mnsbAao8TTMAO3CVJUg9gOHCzEKJnG69bK0lS/5Z/j5/qYgWNmTQ56kn1l7fH67L8A4SbfRkYFiur3VYcTiff7djH6JR4wlVM9nE6JT7+dBOJCeGMGJ6s2rodJT+jiE+e/QanjDVdGn99bnjpSlIHJ/HCNa9TkqP+lJD2MnZMd7rEBPPRx5tOSwA6SpfgQIYmduWbbXsVW3doRDcCTWaW5cv7MJDqP4B6ezVFzdmnbMPjBFOSpCJJkra3fFwH7AcUOwTMqNuBQJDkJ1+dpMVhZ03xESbFpCq2HbvlSD6ltQ3MGqhudLn5t8Pk5JRz0YXDPTa6tFltPH3pK3z23DdUl3p2EoeGZ2HyMvLwJ3fgdDh55vL5OBQcbXU66PU6LpwzjEMZxezclavq2rMG9iCvskaxzj9GnZ4J0cmsKszALuMDb7J/fwAy63aesg2PE8xjEULEAwOAtgpoRgghdgkhfhJCnHLPucz6XcR4J+Fj8D9VE39gU2kODXYrk7ukyGbzeH7YeQBfLxPjeyQptkZbfP7lb0SEBzB+nOc2WF/8+Bcc2nqYO966kZCoYHe7o3GGEZ0Yya2vXcuedQeOjn7zRKac1ZvgIB8+/0Ld7eOzeiXjZdDzg4JjvyZ3SaXK2sT2cvlKfQKMIUR4dT2txB+PFUwhhB/wJXC7JEnHnzBvB+IkSeoHvAr86VUthLhOCLFVCLG1rOz3WywWRxP5jZkk+8tbdL+qMBOz3sCIiHhZ7bZitdv5ZW8mk3omYVaxs8/hI6Xs3JnL7FkDMRiUqSs9XQ5uyeSTZ79hylXjGXOevE0oNDoPky8by7g5I1j8+OdkpcvbeUYuTCYDM2cOYNPmw+Tnn34Xm/biZ/ZiXFoiy/ZkYFco6Wh0VCJGnY5VRZmy2k3270tOwwFsTuspfb9HCqYQwohLLD+UJOmr478uSVKtJEn1LR8vAYxCiLC2bEmS9KYkSYMlSRocHh7+u69lN+zDiYMkX/m2YyVJ4teiTEZGxmM2GGWzeyzrM3Koa7Ywo193Rez/Gd98uw2TycAMD+3qY7PaeOGa1wmJCuLGl65ytzsaZzi3vPp3/IJ8ef7q1zy21GTWOQMwGHR8851yfV7bYnq/7lTUN7I1S5lmD/5GLwaHdWNVobyCmejXF7tkJa/x1M5HPU4whetg7B1gvyRJL/3Ja6JaXocQYiiun6Oio2tlNexFLwx09ZVPeLLrq8htqGZclHJbpcvSMwjw9mJ4cjfF1jie+oZmVqzcx+SJPQkMUK6J/Onw6bPfkr03j9sXXIdfkK+73dE4wwkKD+SW/1xLxvYsvpr3o7vdaZOQED/Gjklj6bJ0mppOLWo6FcakxuNtNLBsT4Zia4yNTiSjtoyiRvlKWOJ9eyIQZNWfWi2pxwkmMAq4HJh4TNnIDCHEDUKIG1pecz6wRwixC5gPXCSdQspWVv1eYr1TMOnkaxq+ttjVoWJMtDKCabU7WL3/CBN6JGHUq7ctunz5XpqbbcyaKW82sVwUZBbx0ZNfMv7CkQw7e5C73dH4izD2/OEMnzmI9//1GaV58s5qlItZMwfQ0GBRtZGBt8nI2LQEftmbKet0kWNpDTrWFctXXuKt9yXKHE9Ww75T+n6PE0xJktZJkiQkSep7TNnIEkmSFkiStKDlNf+RJKmXJEn9JEkaLklSh4edWZ3NFDYdId6vrYqVU2d9STbdfIOI81Mm2WRrVj61zRYm91KvpEOSJH78aScpKZGkpkaptm57kSSJ1+YuxOhl5AZtK1ZDRoQQ3PzKNUiSxIK73nO3O23Sp3cscd1CWfKzug3kJ/VMpqK+kd15xYrYTw0MJ8zsy/qSbFntJvj1JL/xEHZnxxsjeJxgqkV+YwZOHMT5yJftaXc62VSaw4jIeNlsHs+q/UcwGw2MUHE7NiOzhCNHypgx3TPPLjf/uJ0tP+3g8kcvIDRay4rVkJeo+AgufvA81n6xiR0r093tzh8QQjB9Wl/27SsgJ0e9KHhsWgIGnU6x3rJCCEZFJrChJFvWms84357YJCuFTR2PXDutYOY0uLr9d/OR7/xyb1UR9TYLIyPla7F3LJIk8euBIwxP7oa3SZmEorZYuiwdo1HPxPHyRuNyYLfZefPeD4hNjeb/bp3ubnc0/qJccNdMIuPCefOeDzyyGcbkyb3R6QTLflGuz+vx+Ju9GJTQhTUHlZvPOSIijgpLAxm18j0ItN7zTyXxp9MKZm7jAcK9YvE2yNclZ1Opq4B4eIQy0d/h0koKqmoZ110ZQW4Lu93BylX7GDkiBX9/s2rrtpef311F3oEC/vHs5RhUHp6t0XkwmU1c89QlZO7IYsWHa93tzh8ICfZl6JBEflmxV9VZmePSEsksqaCgSpkGIa27dZtKs2WzGWAMIdgYQW5jx+tIO6VgSpJEfmOGrNElwJayXBL9QwkzK9Oqbt2hbABGd49XxH5bbN2WTU1NE5MnnXJvCMVobrTwweOf02tUd0bMGuxudzT+4oy/cCTJAxJ4/9FPsVrkawwuF5Mm9qKsrI709DzV1hyTGg/A+kPK1Kp28Qkk2ieALWXy/kyxPinkNXY8w7dTCmaVtYRGRx2xPvJ14nFKEtvK8xkSrtyYrfUZOSRGhBATFKDYGsezavU+/P3NDB3ieVNJvv/vMiqLqvj7U5d6bJs+jb8OOp2Oa566hOLsMpa+u9Ld7vyBUSNTMJuNrFx1ahmgp0JCeDAxQQFHH+blRgjBkLCubCnLlfUcs6tPKjW2cupsVR36vk4pmAVNrkPqWB/5Mk0za8uptTUzKEwZwbTY7GzPLmCkisk+VqudDRsyGTUyBaPRszr7NDda+PyFbxk4uQ99xqjbT1ej8zJ4Sj96jkjl42e+xmb1rCjTbDYyfFgSa9cfUm3slxCCESnd2Hw4T7GuP4PCYilrbqCgUb5t3y4t9/5WLWgvnVYw9cJAhJd84rajpefhwDBl+sTvyiui2WZnWJJ6grljZw4NjRbGjvG8vrE/v7uSqpIaLn34fHe7otGJEEJw2SPnU5ZXwYrFnneWOXZMGtXVjaTvUW9bdkRyN+otVvYVlipivzUIkbOvbLQ5HoGgoLFjnYQ6pWAWNh0h0twNg06+TNOdFQUEmbyJ9wuRzeaxbDmSj04IBicoNrjlD6xbfwgfHxMDB8SptmZ7sNvsfPHi9/Qa1Z2+Yz0vc1fjr83gqf1J6h/Pp8953vi4YUMTMRr1rFuvXAee4xmc4BphuOWIMiKdEhiOt97IzopC2Wx66b0J9YqhsLljGb6dTjAlSaKoKZtos7yZpjsrC+kbEq3YWdqWrHzSosMJ8FYnU9XplNi4KZMhgxMxmTwr+3TdV5spySljzj2z3e2KRidECMGF9/4f+YeK2Pyjuj1cT4a3t4lBA+PZuDFDtTmZ4f6+JIaHsC2rQBH7Bp2OPiHR7KqQ136MOYHiJk0wT0idvYpGRy3R3vGy2Wy0W8msLadvSIxsNo/FaneQnlfMIBWjy8zMEiorGzxySPTX85cQkxzF8HO0Fnga7mHM34YRHhvK1/OXuNuVPzBieDJFxTXk5Ha4vfYpMzA+hu05hYq1yesTHM2+6hJsTvma4Ed5x1Nt61h9Z6cTzJJmV/pzpFm+bcb91aU4JYneIcq0jTtQWEqzzc6AOGUEuS02/3YYIfC47NjMHVns23iI2TdNQ6frdJevhodgMBqYeeNUdqxIJ/eAMpHVqTJsqKsH62+/KdOBpy0GxnehrtnC4VJlxoz1DonG6nSQWSNfA4OoU9CATnfHKWl2NRc4lV/Wn7GvytVLsXdwtGw2j2Vny2RzNQVzy9YsUlOiCAryUW3N9vDDG8vx8jZx1pXj3O2KRidn2jUTMBj1/PjGcne78jsiIgKIiwtjy1blOvAcT/9urnvTzlz5zhmPpXewKxjZWyVf39pIc8cTKDudYJY25+NnCMLH4C+bzf3VJQSZvInyls/msezOKyYq0J+IAGUaIhxPY6OF/QcKGTgwXpX12ktTQzOrPl7H2Dkj8A9W53ehofFnBEcGMfL/hvLL4jUe18hg0IA49uzNx2q1q7Jet9BAgnzMpCvUiD3ePwRvvZH91SWy2Qw0huGl69iows4nmJY8wr1iZbV5sLqUtKAIxRJ+9uQX07erelNC0vfk43A4GTggXrU128O6rzbTWNfEtKsnutsVDQ0Apl09gdqKOjb/sM3drvyOAQPisVjs7N+vTMR3PEII+sRGKSaYOiFIDQxnf418pStCiA5rQacTzDJLAWFe8m1tSpJERm05qYHhstk8lpqmZvIqa+jZJUIR+22xa3ceer2OXj3VSzJqD6s+XkdkXLjWqEDDYxh4Vl9CooJY+fE6d7vyO/r17YoQsFvFNnm9YiM5XFpJk0INHVIDw8moKZPVZri5Y/e4TiWYTslBs6OBcC/5hKCwsZYGu5WUAGUEc39LMXDPmEhF7LfF7vQ8uqdGYTarNxHlZFSX1bBt+W4mXDxaa4On4THo9XrGzRnJ5h+20VDT4G53juLnZyYxIYJdu3NVW7NnTAROSSKjWJkRYymB4VRaGqlolu/3nOI3oEOv71SCaZdcTz6hXvIl52S2jJ1JCQyTzeaxHCxy2e8Ro4wgH4/Vaicjo5g+fZTriXsqbPhmC06Hk/EXjnS3Kxoav2PcnJHYrHY2/eBZNZm9e8ey/0CRam3y0lruUQeK5I0CW0kOcN1jj9TJVy7TL3hMh17fOQXTJN954JFa1x8vwT9UNpvHcqi4jFA/H0L81MlWPZRRjM3moGcP9TJy28ParzYRkxRJYl/P6jqkodFjeAqhMcGs/WqTu135Hb16dqGpyUpWljICdjwxQQH4eZkUF8xMGWdjdpROJZgOpytjLMgk33lgVl0FAUYzoV7KCFpGcQWpUcpEr21x4KCrhKVnD885v2ysa2LXqr2MnD1U247V8Dh0Oh0jZw1h29JdWJut7nbnKD3SXA+9Bw4VqbKeEILkyFCOKFSLGe0TgEmnJ7uuYxNG5KRTCaZdsuFvCMGoM8lmM6e+inj/YEVu5E6nxJGySpIilOlP2xaHDhUTGupHaKjnlG1sW74bm9WudfbR8FiGzxxMc6OFXb+qN1rrZMTEBOHvb+bgQXUEEyApMpTMUmU6DOmEIM4vmOx6ZQS5XT64bWU34JDsBJvkPQvMra+im1+wrDZbKamtp8lqI1FFwcw8XEJKinoJRu1h27JdePuZ6TVK3oHfGhpy0XdcT4wmA9uW7XK3K0cRQpCcFEnmYWWmiLRFYngIVQ1NVDc0KWK/m18wefXVithuD51OMAON8m1v2p1OChpr6OobJJvNY8kudz1JxYepI5hWq53c3AqSEj1LMHes2E2/Cb0wGD2rCbyGRitmHy96jU5j+y+73e3K70hOiiArq0y1xJ+EcFfwkFWuzLZpV98g8hqqVGssfzyaYJ4GpU11OCSJWIUEM7fC9SQVF6aM/T+sl1uB0ymRlKhORm57KMuvoPBwCf3H93a3KxoaJ6T/hN5kpedSW1HnbleOkpgYgdVqp7BInagsLtQlmK33LrmJ9Q2i0W6j2qpMBHsyOpVgSkgEGOWL1longMf4BMhm81hyK2rwMuiJ8FfnPDEr25XdFh/vOYKZvnY/4Nry0tDwZPq1XKN71h1wsyf/Iz7OFSColikbHIBOCPIUEswYX9e9Nr+hRhH7J6NTCSaAv1G+88aiRteTZLRCgplfWUOX4EB0OnUyQ3PzKtHpBF1ilDmTPRX2bTiI2ddLKyfR8HhSBydhMOrZt/Ggu105SrdurnK3vDx1Rn2ZDHoiA/0oqKpVxH7rvbakyT1RfOcTTIN8YlDc5LoolGq6XlhVS3SQMrbbIi+vgpjoIIxGvWprnoz9mzPoPiQZvcFzfNLQaAuT2UTygAT2bTrkbleO4u1tIizMn7x89TJLuwQHKCaYrffa4kZl7J+MTieYfgb5zgPLmurx1hvxM3rJZvNYimvqVBXMwsIqunRRLyP3ZNisNrJ259B9cJK7XdHQaBcpg5I4vCMbp0KDlE+FLjFBFBaql1kaFehPcY0yEWColy86IShtrlfE/snohIIZKJutsuYGws2+itRgWu12KhuaiApURzAlSaKoqIboaPl+P6dL7v4CbFY7SQMS3O2Khka7SB2USGNdE4WH5RtDdbrExARTWKResX9koB8ltfU4nfJnsup1OkK9fCiTsZ9sR+hUgikAs95XNnsVlgZCzfLZO5byukYA1WZg1tdbaGi0EB2lTkZue8je45q0oJ1fapwpJPRxDSXO3qNe0/OTERUZSGVlg2qzMSP8/bA7nFQ3KpPJGmb2pVITTOUR6GWNBiubGwlRqCVeeZ3rggjzV6eHbGmZ60wgIkKZBKZTIWdfHnqDni4p6s0C1dA4Hbr1dM1XzNmX72ZP/kfre7qsTJ1EmdZ7VlmdMqIW4uVLhaVREdsno1MJpk7I++NWW5sI9urYxO72UtHguiBCVWq63vpmCgtT78z0ZORnFBGdGIHR5DljxjQ0ToS3r5mwLiEUZKjXju5ktL6ny8vVEcxQP9euW5VC3X6CTN5aHaYaKCGYgSZlBLP1Ygv2Vcb+8VRWug7RPamHbGFmMTHJWnSpcWYRkxxFQWaxu904Sut7urxCnUSZYF8zAJWKCaaZaosmmIojZPxxrQ4HzQ47AUazbDaPpaaxGYAgH3UEs6rKtX0SEqzMmeypUJJdRlS8fJNlNDTUICohgpJs9fq3nozW93RVtTrnfoEt96zWe5jcBJjM1NksbmmP16kEU84Is87muhj8FSopqW2yoNcJfFTajqyuacTb24TJ5Bn9WhvrmqivbiC8q3qjzTQ05CCyWziVRdXYbeok2ZwMf38zOp2gpkadqCzQ2xVE1DYrI5j+Ri/skpNmh/q/304lmHJGmA1219w7X6N8o8KOpbbZgp+Xl2rzH2trmwgIUCZaPhUqCl2F1mEeVBeqodEeQmOCkSSJymL3TdU4FiEE/v5mamvVEUyTQY+XQU9ds0UR+74G1z233qaM/RPRuQRTRvFpstsA8DMoE2E2Wqz4mZUR47aor7fg7+c5gllV4uoVGeJBZS4aGu0hONJ1zVaXuqffaVv4+5mpr1cm4msLXy8TjRabIrZ9WgSzyaGM/RPRuQQTGQWz5Y/lpVdmC7PRasNbxezQxkYL3j7qCfTJqGnJ6AsM95wyFw2N9tB6zdaUuad9W1v4+HjR0KBeROZjMtJgsSpi29vgui+2Bi1q0skEU74ft3X/3KyQYDbb7Hgb1RPMpiYbPt7KRMunQn2VK6PP34OSkDQ02oNfyzVbV+We4vq28PEx0dysnsCYTUYsdmXOGFvvuRbtDFNZ5IwwrS1/LJNCgmmx2TGp2HDcYrHh5eUZCT8AjS3nLT4B6tShamjIhW+g65ptqHFPcX1bmEwGVQXTy6DHYnMoYtukc92nrE5l7J8IjxVMIcQ0IcRBIUSmEOL+Nr7uJYT4tOXrm4UQ8Sc3Kp9/dsnVXNkoc21nKzaHQ1XBtNocHpMhC9Dcsn1k9vWcqFdDoz2YfVzXrKVR/aSUP8NkMmC3qycwRr0em0OZ9Qw61z3XpgmmCyGEHngNmA70BC4WQhw/QfjvQJUkScnAy8CzJ7Uro2LaW6YR6HVKCabz6IWhBna7A4PBcy4HS5MFnV6Hweg5Iq6h0R5M3q5cAEuTMmd4p4LRqMeqUMTXFga9DrtDmYkt+pYgpTVoURPPuUP+nqFApiRJRyRJsgKfALOPe81s4L2Wj78AJgm1ajAACVfRrF6hJSVJUm1wNIDTIaHXe87l4LA7tRmYGmckhpZ5sk6754z40ukEkgLTQ/50PaHDqVBjgVbBVMr+iTjpHVIIcYsQQr6py+2jC5B3zP/nt3yuzddIkmQHaoDQExmVM+mn9W8lZ9T6O/vIWwZzMpySpOp6J0NyOlV9YNDQkAtdy86QJ83EFEKo6o8Qygla623KIwUTiAK2CCE+azlXVOMu1tYax/922vMahBDXCSG2CiG21jXI13y49bcg/XFJeeyDqq2fPEgrARA6nVtaX2lonC6twqRT8UilPQgVH0AlCXSK7b65/quU/RNx0r+oJEkPAynAO8BVQIYQ4ikhRJKCfuUDXY/5/1ig8M9eI4QwAIFA5fGGJEl6U5KkwZIkDfbzla9EoTWydCj2FCUUGcD6Z+h0OhwKnTmcCjq9DocHbWlpaLQXR0tyjc6TjjgcTlUFRpIkxR7CnS1Bijue8dv1F5Vcj/rFLf/sQDDwhRDiOYX82gKkCCEShBAm4CLgu+Ne8x1wZcvH5wMrpZOEJHJGg60JOQ6FDp4NOh0OFbdQjAadqll0J8NkNuKwO3AolGmnoaEU1pbyjdbkH0/AbndgVDGBzuZ0KJa02HpfNOjUz3FozxnmbUKIbcBzwHqgjyRJNwKDgL8p4VTLmeQtwFJgP/CZJEl7hRCPCyFmtbzsHSBUCJEJ3An8ofTkj4bl8/FoppZComY06LCpGPEZjHqsVs8RJ3PLiKBmFbuTaGjIQWs5iZcHCabN5sBgVC/itdmdGPTKCJpNct2njG7Y8m7PI0cYcJ4kSTnHflKSJKcQ4hxl3AJJkpYAS4773D+P+bgZuKBDNmVUTFPL041SxbMmg4F6hZoXt4WXlxGLQr0fTwXfANeIoMbaJny15gUaZxCtDQtaGxh4As0WG2Yv9TqHWe12zApFtNaWXSeTJ0aYkiT983ixPOZr++V3STnkFMzWHrLNCjUANhsNNKs4Hsjb20iTB9WNtd5s6lWa4aehIRf11S7B9AvyIMFstmE2qyeYzTY7XgaFBNPZ0mVNp36NtuecSquAhHxbnN5618WnVD9DH5ORJqt6EZ+vjxeNHiSYrQ2sa8vly2zW0FCD2nJX0/WAMM8ZHNDQYMFXxa5ZjVYbPgpFtK1N11ubsKtJ5xJMGTNaW/9YjQp1zPf1MlGvULf/Ntfz9aK+3nPOC4MiAgGoKvGMmYIaGu2ldTRdkAdN2qmvV1kwLVZ8FJq21Ngyi1gTTIWRc0vWr2VwdINCQ0z9zCbqmi2q1SIGBHirNmC2PYTGuHpllBf8oVJIQ8OjqSisAv53DbsbSZKoq2sioCUvQGlsDgdNNjv+ZmUEur5FMJWaRXwiOpdgylgC4m90ZXHWKiSYAd5m7A4nTSqdYwYGeNPQYMGmYr/JE+EX5IvZ14vS3HJ3u6Kh0SHK8soJDPPHpOIA+BPR0GjBbneqJph1Ta57YoBC4wLrbRZ0QmgRptI4ZTzD9NIbMOn01CkkmIHeLkGuaVRnSnpwywy/ag8ZSSSEICo+gpKcMne7oqHRIYqyS4lKiHC3G0eprnK9p4OD1JktW91yzwr0UUaga60WAoxmz+z081fCKXOTgUCTmWqrMtuYwb6ui626UZ1t0pAQ15upsqJelfXJXpLAAAAgAElEQVTaQ1RiBIWHi93thoZGhyg6XEJ0YqS73ThKRct7OjTUT5X1qlruWUE+ZkXs11ibCDC6Z+xfpxJMCXm3G4NMPlRblBG0kBbBLK9TJ+ILb8noK/OgrNSuqTEUZBRr3X40zhisFhsl2aXEpsa425WjlFe43tNhKglmZb3rnhXqp0xZTZW1iSAvdbaXj6dTCaZTcsqaRBNi9qHSooyghfm7Ir6KenXqEMPD/QEoLatVZb320K1HLDaLjZJsbVtW48wg/2AhTqdE17Tjhyu5j5JS13u69T2uNK0P+WEKCWalpZFgL/fUuHYqwZSQsDjliwhDvXwob1ZG0MJbBLOsTh3BDArywcvLQElxjSrrtYf43q7++1npuW72REOjfbReqwl9urnZk/9RUlxDgL8ZHx91tjHL6hrQCUGIQoJZ0dxAmJc657HH06kEE6DBLl8EFWb2pdyijKB5m4wEmL0orlHnTFEIQVRUEIXFnlP3GN+7GzqdIGP7EXe7oqHRLjJ3ZGH0MtK1u+dsyRYWVROtYolLSW0d4f6+6BXo9SpJEhWWBsK91dlePp5OJ5j1dvkEIcLsR73NcrSQVm6igvwprlHvTLFLTBAFBVWqrXcyzD5edOsRy6FtmmBqnBkc2naYpH5xGFScDHIyCouqiYkOUm294uo6ogKV2f6tsjZhczoJM2sRpirIKZiR3q6LoqRJmSgwOsifwir1zhRjY0MoKKjyqLmYaUOTObA5QxsmreHxOOwODm05TNrQFHe7chSr1U5JSQ1du4aotmZBVS0xwcoIZkmjK4CI9nZPF6VOJ5i1Nvk6x0T5uP5oRY3KiFpscCD5lTWqiUW3rqHYbA6KSzznHLPnyO7UVdaTd/D4+eEaGp5FVnouzY0WeoxIdbcrR8kvqHQlIcWGqrKew+mkqKaOLsGBitgvanLda6N81ElgOp5OJZgCIatgxrQIZmGjMgLTLTSIRquNygZ1ajHj48IAyM72nO46fcb0ACB9zT43e6KhcWJ2/+q6RluvWU+g9b0cHx+mynrFNXXYHU66hiojmAUNrntt671XbTqVYOqEnhqbfGIQ7ROA4H9/RLnpFuo6d8itUCcRp/VNlZXlOWUcXVKiCYkOZufqve52RUPjhOxcvYeYpEjCVYrm2kNWVhk6naBrrDpbsjnlrntV671LbgoaazDp9ISZtaQfxdELg6yC6aU3EOntT16DMoIWF+bKbMsuUycRx8fHi5iYIDIPl6iyXnsQQjBgUm92rkjH6fScs1UNjWOx2+zsWrWXAZP6utuV35F5uJT4uDBMJnWSkLJa7lUJYcpk5ebVVxPrG+SWtnjQyQTTIAzUWOXdbozzCya3XhlB6xIcgFGv53BZhSL22yI5KdKjBBNg0OR+VJfVkrkjy92uaGi0yYHNGTTWNTHoLA8TzMwSkpLU62ubVVaJr5fpaOMVucmtryLWV5nt3vbQqQRTL4zU2MpxSPK1WovzCya7ThnBNOh1JIQHc6REvRFXqSlRFBZWU1enTtP39jBken+EEGz+Ybu7XdHQaJON329Db9AzcHIfd7tylLLyOioq6+meGq3ampmlFSRFhCAUiAAlSSKnvooEf/dteXcqwTQII87/Z++8o6K6uj783Bl6r4IgIggIKooNe+8llqjRJBrTE2tMTDG9d2N6Ykk0aiwxsffeOyoiKFVBFFA6DDDAzJzvDzSf8dUoeO8MxnnWmqULZvbewMz93XPOLhgorJDvjK6Boxu55SUUVygjMA3ruJN02XgrzNBGVR+u+Pjak5Xq4ulMWPsQDq49ZupQzJj5H4QQHFxzlGZdG2PvbJr6wJtx7TPcqJFxBFMIQcrlXIK8lBG0bK2GEl0FDRxNN2f0vhJMtapqHz+vQr4JGIFOVW+Oc8XKiFqjuh5kFBRRrFVmjNiNhIbWRaWSiDt7ySj+7pROw9qSfPI8medq13axGTOpcelcTMyk84NtTR3KP4g7cwlLSzXBQcaZnJJTXEJeSRmNvD0VsZ9SVHWNbehonIzfm3FfCaaFVDVwNKc8UzabQU5Vf7ykImVKMa69+RIyjZO5amdnTUADT2JjLxrF353SeXjVxWjPn4dMHIkZM/9k75+HkCSJjsMiTR3KP4iLu0RwsLfREn7iM6uugSF1lRG0lKvX2GuLFFlsak5X6/n3lWCqJQusVDbklMu33ehn74qVSk1SoTKCGeZTJZhnM64oYv9mNGvmx5mzGeh0tWeslneDOjRuH8KuZftNHYoZM38jhGDn0v1E9GiKm7fptgpvRKutJCExk2bhfkbzee0aFeajTJJRYmE2DpbWeNvK17QgpmBftZ5/XwkmgLtVXXLK5dtutFCpaOjkTmKhMoLm6eSAp6M9cReNtxXZLNwPrbaS+AT5VuJy0P3hTpw7lca5mDRTh2LGDADxR5PJSM6i++iOpg7lH5w5cwmdzkDzZsYTzLhLl/Fzc8bRRpmpKElFOQQ7eciaUFTdxdN9J5h1bPzILpd3u7GRsxcJCgkmQLifN7GXjCeYEc2rRhOdjK5dwtTj4U5YWlmwed5OU4dixgwAW+btxMbOmi4j25s6lH9w4mQaarWK8Kb1jOYz9mIW4X7eitgWQhBfcIUwF3nPY69o06v1/PtQMOtRUJlDuV6+dnOhLnW4XKYhV6HZmOH1vDmfnU9BqXFKPZyd7QhqWIcTJ1KN4u9OcXJ3pMPQNmz/fS/lZcZJgjJj5laUFpexc+l+Oo9sh72TaQYa34rjJ1MJbVTXaDMwLxdqyCrUEF5PGcHMKC2iqFJLqIt8270aXQGl+upNg7rvBNPLumr1dFkr31DiJq5Vb5IzBcqsAiP8q9LCYy4Yb4u0dasAYuMuUVpau4Rp4LO9Kc7TsPfPw6YOxcx9zo7F+yjTaBn0XB9Th/IPCovKSEzMpHXrAKP5jL5QtbUZ4a/MHNC4/KrKhmvXWjm4XM3VJdyPgmmjhGBWbRPE5ikjaE3reWOhUnEyzXi1kZGRgej1Bk6crF3bshHdm+IX6svqHzaZR36ZMRlCCNb+uJmGEQ0Ia1t7xnkBHDt2DiEgsnWg0XyeSM3A2kJNaF1lSkpO52eiliQaOcu3wswqS632a+47wXSxqoO1ypZMbapsNp2tbPF3cCVGIcG0s7IkzKcOx1ONVxvZtEk97O2tOXQ42Wg+7wRJkhg6qT+JUSmcOZRo6nDM3Kec3HGa1Lh0hk0ZoEhXm7vh0OFkXF3tjdawAOBE6iWa1a+LlYVaEfun8zIJcfbE1sJSNptZ2lTsLarXZu++E0yVpMLbpgFZZfL2JW3m5kNMnnIrwNYBvsSkZ6Gt1Cnm43osLNREtgnk8OHkWjVQGqD3uK44ujmw/Ms1pg7FzH3KH1+sxs3bpdZlx1ZW6jl69Bzt2jZEpTKOkBeVaYnPzKZ1A19F7AshiMnLINxN3u3ezLJU6tpUb9v6vhNMAB/bADK1qRhk7Ckb4e5LVlmxYsOk2wTWo1KvJ9qI27KdOoaQX1DKmVrW9cfW3oahk/pzcM0xUuOqfw5hxszdkBCVwontp3lw6iCsbKxMHc4/iI5Oo6S0nE4djTfE+kRqBgYhiGyoTAlLqiaPwgotLdzlE2SdoZLL2gv42JoF87b42DakwqCVteNPy6t/zJO5yohL64B6WKhUHE6R7+z1drSNDMTSUs2evQlG83mnDJ3cHxt7a5Z8ssLUoZi5z1j80V84uNgz6Pnepg7lf9izLwFbWytatvA3ms/DKRewtlDT3E+ZLeDjOVVlgBEyCmaWNg0DenxsG1brdfelYPraVf2SLpUlyWYzzNULW7Ulx7OVWfHYW1sR7ufNoWTjCaadnTWRbQLZuy8Bg6F2Jdg4uTsyZGI/di87SNrZ2tXGz8x/l6QT5zi0NooHpw6sdaUkOp2e/QcSad8uCGtr+c76bseh5Au0auCLtaUyLfiO51zEydLm7zakcnCpLAX4fy24U+5LwfS09sVKZUN6qXwJLZYqNc3dfTiWo9wWYYdgf+IuXSa/RL4a0tvRrWsYOTnFnD5d+7Y+R0x7AFsHG357e5mpQzFznzDvzSU4ujnw4AsDTB3K/3D8RCpFRWV07xZqNJ+ZBcUkX86lQ7ByK9qo7HRaedSTdWj0xdJE7NROuFpWL+v2vhRMlaSmnm0Q6aXyZllGetbnbMFlxUZ9dQppgBBwIMl4pR4d2gdhY2PJ9p1xRvN5p7h4OjNi2gPsX3mEM4fNGbNmlOXkztNEbTnFw68/WKvGeF1jx84zODraENmmequmu2F/YipQdW1SghxtCeeKc2njKe/5aHppEn52wdXOcL4vBRPAz74RWWXnqTDIJ26RnvUxCKHYKrOJbx3c7G3ZGy9vhu+/YWtrRedOIezeHU95eaXR/N4pI14ahJu3C7OnLTDXZZpRDIPBwJxXFuHl78mQiX1NHc7/UFJSzr79CXTrGoalpTKlHTdjb8J56ro4KjYD8/CVqsVBuzryrWDLdBqyyy/iZ9eo2q+9bwWzvl0jDBi4KOO2bEuPelirLTh0OVU2m9ejVqno3CiAfQnnqdQbb5JI397hlJSWs/+AfGe+cmHrYMu4D0Zz5lAiu/84aOpwzPxH2frbbpJPnufJTx6pdZmxAHv3xVNerqNP76ZG81leqeNQUhpdQwMVq0U9dDkVBwsrmrjKl1B04erOYn17s2DeMfWv3l2klcTLZtNabUErj3ocVEgwAbqHBVKkLedEqvHKSyIi/PH2dmbT5lNG81kd+j7RjeBWgcx+eQGlxcY73zVzf1Ccr+GX6b/TpGMjuo3qYOpwbsrGTTH413encZgyreluxuGUC5RV6ugeplxHoYNXUmlbxx8LlXxSlVZyBhVq/Oyq36HpvhVMOwtHvGzqk1pyRla7nbwCiC+8QnaZRla71+gY0gBrCzU74ozXgUelkujftxknTqZxKSPfaH7vFLVazeQfniY3I5+F7y03dThm/mPMe2MJxXkaJv/wNCoZL9xycT41m7gzl+jfr5lRuw7tOJOCvbUVkYHKTES5oMnngiafDl7y9sRNLTmLj20gViqbar+2Vv31JUn6UpKkeEmSYiRJWiVJksstnpcqSdJpSZKiJUmKqqm/BvZNuFAaj17I1z2nk3fV3da+rHOy2bweOytLOoU0YHtcslFLPfr3a4ZKJbF+Q7TRfFaHsLbBDHymF6u+3UDSCWV+92buP2IPxLN+9jaGTRlAw+YNTB3OTVm77iSWlmr69gk3mk+d3sCOuGS6hQZiZaFMOcm1a2gXb/lWsBWGci6WJRHg0KRGr69VgglsA5oKIZoBicDr//Lc7kKICCFE65o6C7BvQoVBy6XSlJqa+B/CXLzwsLFnT5Z8Nm+kT9NgLhdpOJVuvOklHh6OdOoYwqZNp2pl8g/A05+PwcXLhRlP/kRlRe2M0cy9Q3lZOTOf/hkvf0/GfTDK1OHclJKScrZtj6Vb11CcnY1XF3r0XDoFpVr6hCvXeH5vZgq+ds4EOLrJZjO9NBG90NHAvnGNXl+rBFMIsVWIv5d7hwFFp58GXr3LOFdyWjabKkmii3dD9mWdQ2dQpgdrt7BArC3UbI4xbgeeYUNaUVSsZcdOebex5cLBxZ4Xfn6GczFpLP7Q3AHIzN3x29t/kJ6QwUtzn8fWwdbU4dyULdtOU1pawbChNV431IjNMYnYW1spVk5Srtdx8Eoq3eo2lHWbOUUTgwrVf0Mwb+BJYNMtvieArZIkHZck6dl/MyJJ0rOSJEVJkhSVnZ39j+/ZWzjjbdOAlOIYeSK+SnefIAortJzIUaYDjYONNZ0bBbApJhGdERujN2vmR2CgJytWRtXaEo4Og9vQ+7GuLP1slbk200yNObU7jhVfr2fgs71p2auZqcO5KXq9gVWrjtM4zIdQI04mqdDp2BabRI+wQGwU6u5z5EoapbpKuvsEyWr3nCaGenbB2Khrtho3umBKkrRdkqTYmzyGXPecNwEdsPgWZjoKIVoC/YGJkiR1uZU/IcQcIURrIURrT8//ndUW5NCctNJ4KgzyDUru7B2IpUrFjgzlyjAGRoSSqynlSIrxOvBIksTI4ZGcT83mWJTxakGry8Rvn8CznjufjfmOkqJSU4dj5h6jKK+Yz8Z+h2+wN8/NGGvqcG7JgYNJXMrIZ8TwSKP63ZeQSpG2nIERYYr52JGRhK3aUtaEnzKdhoulKTR0aF5jG0YXTCFELyFE05s81gBIkjQOGAQ8Km6xjBFCZFz99wqwCqjxOybYsTl6oeO8JramJv4HR0tr2tVpwNZLCYqtxLo2CsDJxpo1J4y7Pdqje2M8PBxZtvywUf1WB3tne6b/PoXLadl8O35OrV0Nm6l9CCH46qmfKbhSyOuLX6i1W7FCCJYtP0zdui507mS8ySQAa0+exd3BjvZB9RWxbxCC7ZcS6ewdiLVavhVsiiYGgYEgx3tIMP8NSZL6Aa8Bg4UQN10aSJJkL0mS47X/A32AGqudv31jLCUrkorlzf7s49uIC5p8Eguzb//kGmBtaUH/5o3YcSaZYq18q+PbYWmpZuTwNkRHXyDuTO0a+3U9TTuGMu79UexaeoD1s7aaOhwz9wh/fbWOg2uO8cznYwlpZbwWc9XlZHQa8fGZjH6oLWq18S7j+SVl7I4/x6CIUCwU8huTl0FWWTF96lW/scC/kVh8EhuVHX52Nb/BqFWCCfwAOALbrpaMzAKQJMlHkqSNV5/jBeyXJOkUcBTYIITYXFOHliorAhyaklh84m5j/we9fUOQgM0X5WuMcCNDWzZGW6ljk5GTfwYNjMDJyZbFS2p3Z53R04cSOaAFP02dz5lDtW9EmZnaRfSuWH55fTGdh7dlWC1srn49vy85iJubvVFLSQDWnTyLTm9gaKualWXcCZsvxmMhqegh4/mlEILE4pMEOTZHLdW8dWCtEkwhRJAQwu9quUiEEOL5q1/PEEIMuPr/c0KI5lcfTYQQH9+t30aOrcityCSnXL7uOZ62DrTxrM+m9LOy2byRcD9vgr3cWXFMvu3kO8HW1oqRw9tw+EgK8QnGK22pLiqViumLplCnvgfvj/iKnEu5pg7JTC0lK/UKH42aSb2Qurw8b6JRGwBUl5jT6URHX2DUQ22xslIm6eZmCCFYERVLeD1vQrzlG7V1o4/N6fF09A7A2Uq+7fBM7XmKdXk0cmx1V3ZqlWCaikZOVb/E+KJjstod4BdGUlEOCQVXZLV7DUmSGN6mKbEXL3M2Qxkft2LokFY4Odrw24J9RvVbXRxdHXhv5SuUFZfxzpDPKStRZpKMmXuXksIS3n7gM3SVet5b+Qp2jrXz3BKqBGXe/L24udkzeFALo/qOvpBJ8uVchrdRrl9tTF4G6SUFDKgnb0JRfFEUEhIhji3vyo5ZMAFXqzp42/hzVmbB7O8XikqSWHdBudFYg1s2xtpCzfIj8pbG3A57e2tGj2rH0WPnOB1b+2ZlXk9AuD9vLp1KSnQqn4/9Dr0RG9ebqd3oKnV8NPpr0hMyeOevl/Fr5GvqkP6V4ydSiTmdzphHOhh1SDTA8iMx2FtbMaC5vGeL17P+whmsVGrZzy/PFh3Dzy4EB8ubNo+7Y8yCeZUwp7aklcRToiuUzaaHjQMdvQJYf+GMYpmazrY2DGgeyrqTZykqM+7qacjglri52TP3lz21PhO17cBWjP/6CQ6sPsaPk+fV+njNKI8QgpnPziJqyymm/PQMLXsa9zywuhgMgrm/7sbLy4kB/Wue6VkTcjWlbIpJZHCLMOytlZnWojcYWHchjq51G+JkVf0+r7eioCKbjLIUQp3a3LUts2BepbFzWwQGzhQeldXuEP+mpJcUcFyhJgYAj7RvTlmljtXHjVtiYmtrxbixnYiNu8iBg7Vv9NeNDJ3cn1GvDmHdrK38/sFfpg7HjAkRQvDL9MVsW7CHx957iAFP9zR1SLdl1+4zJCVd5olxXYx6dgmw4lgslXo9j7SPUMzHoSupZGtLGOov743LmaKqa3oT53Z3bcssmFepa9MAVysvzhQdkdVuH99G2KotWZUqX/u9G2ns60WEf12WHIpGr1A7vlsxoH9z/Ou7M2fuLiora/9W51OfPkqfx7ux8P3l/PnVOlOHY8ZELP5oBcu/XMMD4/sy5u0Rpg7ntpSXVzL3lz0EBXnRq6dyGao3o1KvZ+nhaNoH1Sewjnx9XW9kVeppnCxtZO/uE1d4iDrWfnhY3/3oM7NgXkWSJJo6tydFE0OZTr7RXPaWVvStF8qG9DNodco1BH+sY0vS8wrZfda4kzrUahXPPduDi5fyWb32uFF91wRJknhpzvN0fag9c15ZyOrvb9V90cx/lT++WMOCd/+g97iuTPr+yVqdEXuNP/86xpXsIiY83wOVyrjxbjmdxJWiEh7reHcJM/9GcWU5Wy4mMMAvTNZmBcWV+aSVnKWpc3tZ7JkF8zqaOrdHL3SyrzJHBDT7+w2hFD0bB+Hr6sT8fcYXrbaRgbRpHcDChQfIyy8xuv/qorZQM33RFDoObcOPL8xjxdfrTR2SGSOx+OMV/DL9d7qN7si0ueNr5XzLG7lypYglyw7RqWMIEc39jepbCMH8vVEEerop1mgdYP2FOMr0lYwMlPdsNrbwEAJBUxezYMqOr20QblZexBQckNVu2zr+1Ld34Y/zys2StFCrGNepJSfTMjiRatwOPJIkMXFCL8orKpk7d5dRfdcUC0sL3vrjJTqPaMesaQtY8slKcyLQfxghBL+9vYzf3l5GzzGdmb5wMmqLmhewG5OfZ+/EYBBMeL6H0X0fTrlAfGY2j3dupejK9s9zpwh28qS5291vm17P6YL9eNnUx8tGnhsNs2BehyRJNHPpzDlNDJrKAtnsqiSJhwIjOHIljfPFyhXPD2vdFBc7G37ZI295zJ1Q38+dkSMi2bItlpjTtbvM5BoWlha8uWQqPR/tzPy3ljJ72gIMRj4DNqM8er2e7ybMZfHHK+j3ZA9emT/xnhHLY1Hn2bM3nkcfbo+3992VRNSEubuPUcfJngdahCrm40x+FqfyMhgVGCHr9nh+xRXSSuMJd+4km02zYN5Ac5fOGDAQUyjvKnNEQHMsJBVLU07Kavd67KwsebRDC/bEnyc+U5ketv/GmEc64OXlxNffbrknEoCganv21QWTGDq5Pyu+2cDnj31PRS0dkG2m+mhLy/lo1Nesn72NUa8O4aW5z6NW3xtiqdVW8u33W6jn68qoh9oa3f+pC5kcSUlnXKdWWFkol5W7LOUkVio1wxrImx0bU7AfgOYuZsFUjDo2ftS1CSA6f4+sdj1tHejtG8KK8zGKJv882iECe2srZu+U9xz2TrC1teKFyX1JS8thybJDRvdfU1QqFRO+eYKnPnmEnUv281rvDyjMKTJ1WGbukrysfF7p8R4HVh1l/MzHefqzMfdEgs81FizaT0ZGAS9O7Wf0MhKAWTuP4GJnw8hI5epTiyvLWZ0Wy8D6jXGxlq/DkhCC6Pw9+NuF4mbtLZtds2DehBau3bhUlswVrbxbi48GtaKgooz1F5Srl3S2teHRDhFsjU0iMStHMT+3ol3bhvTs0ZjFSw5y/rzxV7k1RZIkRk8fxptLp5JwLIXJ7d7g/Ok0U4dlpoYknTh39W94gXdXvMyDUweaOqRqkZCQyZ9/HWVA/+a0iDBuog9ATHoWexPO83jnVoo1KgBYnXqaEl0FY4LursfrjWSUneNKeToRrl1ltWsWzJvQ3KUzKlScyJc3gaVdHX+CnTxZmHRM0QSTcZ1a4WBtxY/bTbPKmzShFw4ONnz+5QZ0untja/Ya3UZ1ZMau9ygvq2BKhzfZ+9e9s1I2U8WOxfuY2umtqk4+ez+g41DjDli+WyoqdHwxYyOurvY8/2x3k8Tww7aDuNjZKNqowCAEC5OiaO7mQ4S7vC0Jj+fvxEKyJNy5o6x2zYJ5ExwsXQhxasXJ/N3ohXwXfEmSGBfSmriCyxzLVi4xxsXOhsc6tWR7XDJxly4r5udWODvb8cLkPiQmZbF46b0nOI3bhfDjsc8ICK/Phw/N5Kep86msMJ9r1nYqtBV8O34On439jkaRQfx47PNaPdPyVvy2cD/nU7OZ9mJ/HBzkaxF3pxxPvcSBpDSe6NJa0dXlvqxznCvO5bHg1rLarTRUEFOwj8ZObbG1cJDVtlkwb0Fr155odAUkFslb1zjUPxwXK1vmJSp7xvhYp5Y429rwzRZ5k5fulK5dQunVswmLfj9Qq0eA3QoPHzdm7HqfoZP7s+q7jbzY+W0yUrJMHZaZW3Ah/hJTOrzJ+tnbeOjlwXyx7R1c6zibOqxqE3M6nT+WH2bQwAjatTW+2Ash+Hrzfjwc7RRdXQLMTzxKHRsHBvg1ltXumcIjlOk1tHbrJatdMAvmLQlxaoWjhSvH8rbJatfWwpJHglqy/VIi54vzZLV9PY421jzbPZKDSWkcTr6gmJ9/Y8qk3ri7O/DxJ2spLS03SQx3g5W1JRO/fZJ3/pzGpaQsnm/xCpvn7zLXa9YihBCs+3kLE1q9SnZ6Lh+seY1nvhiLhaXxk2TuFo1GyyefraNuXRfGP2f8mkuA3fHnOJmWwYSe7bCzUm4aSkLBFfZlnWNMcCusZM5ajsrbhquVFwEO8o8hMwvmLVBLalq69SCx+CQFFfImrzwW1BpLlZpfEw7LavdGHm7XHB8XJ2Zs2ofBYPyLvIODDW+89gCZWQV894O8Nx7GpPPwdsyO/pLgVoF89dRPvDP0c3Iz800d1n1P9sVcXu//Md9N/IWmncOYfWoG7R+Qd3vPWAgh+OrrzeTmanjz9cHY2iq3FXordHoDMzfvp4GHKw+2Vm7mJcCc+MPYWVjyaEN5k31yyjM4VxJLa7eeqCT55c0smP9CG7fegJB9lelp68CDDZqx4nwM2WXy9a29EWtLC17o04GzGVdYF31WMT//RvPm9RnzSAe2botl6zblGtArTZ36nny5413Gz5z9pVIAACAASURBVHycE9tieLrJi2z8ZYd5tWkCDAYDa37czNNNXiRufzxTfnyaTze9iYePco3BlWbd+mj27I3nyce7EBYqb7ebO2VF1GnOXcljat+OWCpYq5pRUsj6C3E8FBAhaykJwNHcLahQ09JVmRW6WTD/BVerOoQ4tiIqbzs6g7xJH0+HtkMnDMxPlHec2I0MaB5K03pefLNlPyXlFYr6uhVjx3SkeTM/vvlu6z1VanIjKpWKB6cOZHb0DBpGNODrZ2cxrdu7nI81zZb3/UjyyfNM7fQWP0z+ldB2wcyJ+YoHxve9p+orbyQxMYsff95OZJtAkzQoACjWlvP9tkO0CahHrybyTgu5kblXd9aeaiTvz1phKOd4/k6aOLfFyVKZmyezYN6Gtu790OgKiCuUN9szwNGN/vXC+D35OAXlZbLavh6VSmL6oG5cKSoxScs8qJpo8vabQ7Czs+LdD1ahKTHuoGu5qRfiw5c73mXaL+NJO3OR51u8wo9T5lGUW2zq0P6z5F8p5Jvn5zCxzWtknrvCawsn89nmt6gb6GXq0O6KwqIy3vtwFa4u9rz+2iCjTyK5xk/bD1NQWsZrg7oqevORXabhj3PRDG3QFB97eZOyTuXvRasvoa17f1ntXo9ZMG9DsGME7lZ1OZS7QXbbExt3pERXofgqs4W/Dw9EhDJ/73Eu5MrXI7c6uLk58M5bQ8nIyOfzLzaY5ExVTiRJot+TPZgf/y0Dn+nF2p8283jIZP6auY4KrWlW8v9FtKXlLPt8NY+HTGbTrzsYPLEf8+O/pdeYLvf0qhJArzfwyadryc3V8O47Q3F2tjNJHMmXc1lyKJoRbcIJ86mjqK+5CYepNOgZHyZvfaQQgsO5G/G28aeBvbxZt9djFszboJJUtPMYQHppEumlibLabuRSh771GvFb0jEKK5RbZQK81L8zlmoVn67bbbJzt2bhfkx4vicHDiaxcNF+k8QgN07ujkz56RlmRc8gpE0Qs19eyOONprDxlx3oKnWmDu+epaK8krU/bWFc8GR+fX0x4Z3DmHt6JhO/fRIHF3tThycLc37ZzbGo80ye1Ntk55ZCCD5auxM7K0um9O6gqK8crYbFyccZXL8JDRzl3TI9XxJLljaN9h4DFb2RMgvmHdDKtQfWKjsOZK+V3faUJp3RVJYzL0HZVWYdJwcm9mrP3oTzbI9LVtTXvzFsaCv692vGwt8PsHuPaRKRlCCgaX0+2/wWX2x/B3cfN75+dhZPhL7Axrnbzc3cq0F5WTlrf9rC4yGT+X7SL9QNrMPMPR/w0brXqR8qbzcYU7Jl62n+/OsoQ4e0ZNAAZesd/40N0fEcO3eRF/t1ws1B2RXunLOHqTDomdREvmbo1ziQvQ57tRPNXTrLbvt6zIJ5B1irbYl070Nc4WHyK67IajvUxYv+9UKZn3iUvPJSWW3fyJgOLQjx9uDTdbvRaE1TFylJEi9M7kPTJvX47IsNnD2bYZI4lKJFj3C+O/gxH61/HWcPR75+bjZjAyey7LNVFOWZzzhvRUF2Ib9/+BdjGkzg+0m/4FnPnc+2vMXXez8kvHOYqcOTlVOnLvDV15toEeHPhOd7miyOglItX2zcS3g9b4a3UbaMJKu0iN9TjjPUP5wAR3dZbWdrLxJfHEWkez8sVday2r4Rs2DeIe3dBwASB7LXyW57anhXyvSVzDpzUHbb12OhVvH+sF5cKdbw7VZlff0bVlYWfPDeg7i7O/DWO3+RmWmac1WlkCSJtgNa8v3hT/l82zs0aOrHr28s4dH64/nmudkkR583dYi1hoSoFL566ice9R/Pgnf/IKRNQ77a/T7f7P+IVr2b3/PnlDdyIT2Xd95fia+PK++/OwwLE87l/GrTXgpKy3jvwV6oVcpKwY9nDmAQBqY0kX8FuD9nHRaSFe08+slu+0bMgnmHOFt50Ny1M1F52ynVybtSCHLyYJh/OIuSo8goKZTV9o00q1+XR9pFsPRwNCdSLynq699wcbHj049HotcbeO31PygoUHZ1bQokSaJlz3A+3/I2c07NoNuoDmxbtIfxLV9lUtvprJu1FU1BianDNDpFucWs/mETz7d8hUmR09n9x0F6j+3KL7Ez+Xj9GzTr0vg/J5QAubkapr+xHAu1io8/GmmSPrHXOJScxsqoOB7v3IrQup6K+jpfnMcf504yOrAFfg7yDsEuqszjZP4uWrh2w8FC+QHbZsGsBp09h1IpyjmUI3/G7NSmXQD4Onav7LZv5IW+HfF2duSdldvQmjAxpb6fOx99OIIr2cW88faflJX9d7NLA8L9mfbrBJZdmsP4rx+nvKyC7ybM5aG6z/DByBns/esQ2nuwfeCdUqYpY9eyA7z34BeM8nmGH6fMA2Did0+y7NJsps5+Dv/GfiaOUjk0JVqmv7GcgoJSPvloJD51lb+434qS8greXbmdBh6uTOjZXnF/M0/vxlptocjZ5cGc9RiEgc6eQ2W3fTOk+6lTSevWrUVUVNRd2ViU+ilpJWd5JXQ21mp5u1R8Gr2DXxMOs7bPUzR2lW/o6c04mJTGM/NW8njnVrwyoIuivm7HgYNJvPv+SlpE+PPxhyNMMizX2AghSIxKYfuivexefpCCK4XY2FnTqk8z2g9uQ2T/Frh6me6iKgc5GXkc23SSg2uPcWJbDBXaStzqutJ9VAd6je1KUIsAU4doFLTaSl57/Q/Oxmfw8QcjaNMm0KTxfLB6B8uPxrDg2Ydo1UDZRKoTORcZuWMBk5t0YmpTeWdTluqK+TL+OUKd2jCq/os1tiNJ0nEhxB31VDQLZjVJL01iVvJr9PUeQ5c6D8oUWRWFFWX02PAzYS5eLOr2iOLbUn9/cJ4ZSauAeor6uh1btp7m8y830LFjMO++NdSkZzvGRq/XE7svnr1/HeLQ2iiyL+YCENwygBY9wmnevSlNOoRg71y7yyk0BSXEHYgnelccJ3bEcO5U1QBuL39P2g9uTZcR7WnSsREqhc/LahMVFTreeW8lx6LO8fabQ+jW1bQJTNdulMd1asmrA+UVsBsRQvDQjoWkl+SzY8AE7C3l7Y+7PWsZu64sZ0rI13jZ1HzItlkwb4Ecggkw/9wHZJad4+WwWVip5D2HWJB4jA9ObmVOp5H09A2R1faNlJRXMPy73xFCsGLKGBxslM0wux2rVh/n+x+30b1bGG9MfwC1+v65sF5DCEFKdCpHN50kams08YeTqKzQoVJJNAivT1hkMCFtgghuGYB/Ez+srJWbKPFvVGgrOB+bTsrJ88QfTebskUTS4i4ihMDS2pImHUJo1bs5bfq3ILCZ/3/yTPJ26HR63v9wNQcOJjHtxf4MHNDcpPEUlmkZ9s0i7K2t+HPyo9goPNFl/YUzvHBoFZ+0HsCohi1ktV2mL2HG2ecIcGjKmAbT78qWWTBvgVyCmVYSz5yUN+hX9zHZ984rDXoGbp6LXgg29nsGa7Wyb+oTqZcYN+dPHmgRxicj+yrq6074488jzJ6zi549GjP91UH3pWhej7a0nDMHE4g7kEDswXgSjiZTUliVIKVSq/AN8qZ+mC++QXWp29AbL38PPP08cPdxxcHFvsZCJYSgOF9DbkY+2em5XE7LJjMli0vJWaSduUhmStbf3ZocXe1pFBlEkw6hNO0USli7YKxtTXvzZWp0Oj0ffryGffsTeWFyH4YMbmnSeIQQvLx0I9vjklkyYTRNfJVtKVimq6TPplm4WNmyuveTsmfh7ry8nB2XlzExeAY+tne3xV0dwfzvHxb9A70sVvztQwlyiGDvldVEuvWV9SzTUqXmrRa9eWLvMn5LPMpzYcp232jZwJdnu0cya+cROoU0YEDzRor6ux2jRrZFrzfwy697MBgEr7826L7anr0RGztrWvZqRstezYCqSR0ZKZdJiU7l3KlULsRf4sLZixzdFE3lDQ0SLCzVOHk44ehqj52TLbYONljZWGFhZYHq6o2IQW9AV6GjvKwCbYmW0qIyivM0FOUWo6v85+fFysYSn4beBDarT7eHOtAwogENIxpQN9DrvlxB3oqKCh0ffryGAweTmDShl8nFEmD18TNsPp3I1L4dFRdLgFlnD5JRWsRXbYfILpZlOg0HstcS5hR512JZXe4vwdSly2aql/doZiVP51DuBrrVGSGbXYAudRvSyyeYH87sZ7B/U+raOclq/0bG92jH4eQLvL9qO+F+Xvi5mTbZ5JHR7VGpVMyZu4uKSh1vvzHkvkgEuhNUKhX1gutSL7guXUf+f4ajXq8nL7OAy2nZZKfnkpeZT/7lAopyNRTnaygtLkOr0VKUq0FXoUOvNyBJVfYsrCywsrHE1tEWD183HF0dcHJ3xNXLBbe6Lnj6eeDl74FbXdf76vyxJpSXV/Lu+6s4euwckyf2ZthQeec91oRzV/L4eN0uIgP9eLKL8vNC0zT5zIk/xAP1mxBZp77s9vfnrEVrKKWX12jZbd+O+2tLtrmNOBZ1AslSnua8C89/QlrpWV5u9DO2Fg6y2LxGuqaAvptn09MnmO87yJtcdDMu5Rcy4rvF1PdwYdFzo7CqBau6lauj+OHH7bRq2YAP3nvQJEN1zZi5UzQlWt56ewWnY9N5aarpzywBtJU6Hv5pKdnFJayYPAYvZ3mvUzcihODpfX9wLDudrf2fw1vmm32NroCv4ifQyLEVo/2nyWKzOluy99ntogpRMkc2a328H6FcX8re7FWy2byGn4ML48M6sDH9LHsyU2S3fyO+rs58NKIPsRcvM2Oj8rWgd8KDQ1vz6ssDOBmdxrRXl1JY+N9rbmDmv0FenoaXpi3hzNlLvPXGkFohlgCfrN1FYlYOn47sp7hYAmy9lMDuzBSmNOksu1gC7L68Ap2hgl7eD8tu+064vwRT7QbaTQidPK3JvG0b0NylCwdzNlBYmSuLzet5NrQ9gY7uvHt8M2U65Rt492wSxNiOLVh8KJqNpxIU93cn9OvbjPffHUZKyhUmT/39P9dGz8y9T/rFPCa/sIiLl/L56IMRdO9WO3rfroyKZUVULM92i6RzowaK+yuuLOeDE1sJc6nD4yGRstvPK8/iaN4WWrn1xMPaNNNd7i/BVHkAVgjNLNlM9vJ+GIGBHVnLZLN5DWu1BR+17k96SQHfxe2T3f7NmNa/My38fXhn5TaSsnKM4vN2dOwQwowvRlNYWMqkKQs5G//fathu5t7ldGw6k6cspExbycwZjxBp4qYE14i9mMWHa3bSrqEfk3or380H4KuY3VwuK+bj1gOwUOCse1vWElSo6OE1Snbbd8r9JZhYgN3DoF2L0F2QxaKrVR3auffnRP5OsspSZbF5PW3r+PNQQHN+TTjM6bxM2e3fiKVazcxHBmJvbcnkRWspLNMq7vNOCG/qx/ffjMXGxpIXpy1hz954U4dk5j5n2/ZYXn51GU7Odnz/zVhCG9U1dUgA5GlKmbp4Pe4Odnw5eoDijdUBorLT+T05irHBrWnuLn/3oPTSJGIK99PRczBOlvLO0qwO95lggmT/NGCBKPlZNpvd6ozARm3PxszfFBnO/HpEL9yt7Zl+dD0VenlKY/6NOk4OfPPoA2QWFvPykg3o9AbFfd4J9eu78+P34wgO8uL9D1ezYNH+v2sBzZgxFnq9gbm/7ubTz9fTpLEvP3w7Fl9fV1OHBUCFTs/UxevJ05Ty7ZgHFJ9xCaDVVfL6sQ342Dnzcnh32e0LIdiYMQ8HCxe6eA6T3X51qHWCKUnSe5IkXZIkKfrqY8AtntdPkqQESZKSJUm641YPkroO2I2GstUIXZosMdtZONLDaxQpmhjii+++McKNOFnZ8EHrfsQXXmHW2QOy278ZLfx9eGdITw4mX2DGptqRBARVU06++vJh+vRuyoKF+3n/w1WU/oeblpupXWg0Wt56ZwVLlx1m0MAIPv90FE5O8vaUrilCCD5eu5PjqZf4YHgfo9RbAnwbt49zxbl80maA7O3vAE4XHuBCaQK9vR+RvX93dal1gnmVr4UQEVcfG2/8piRJauBHoD/QGHhYkqQ7rhWR7J8FLBGa72ULuK17XzytfdmU8Rs6g/wJOr19GzG4fhN+PHOAWCNszQIMb9OUMR1asOjASZYfiTGKzzvBysqC114ZyITxPTlwMIkJkxaSllY7zlvN/HdJOXeF5yf+RtTx80yd0peXpvbD0tL05VfXWLD/BH8di+WZbm0YFBFqFJ/Hcy7yS8JhHgqMoJO3/Oe3FYZytmQuxNumAS1d5V+9VpfaKpi3IxJIFkKcE0JUAMuAIXf6YkntCfZjQLsOUZkkS0BqyYKBPk+SW5HJwRz5h0wDvNuyL27Wdrx8ZB3leuOM5XplQBe6NArgo7U72Z+YahSfd4IkSYx4sA1ffj6a4uIyxk9awI6dZ0wdlpn/IEIINm+JYdKUhZSX6/h6xiMMfkDe3qh3y84zKczYtJfeTYOY0rujUXyW6ip45cha6to68UZEL0V87L2yioLKHAb5PIVKkufm5G6OzWqrYE6SJClGkqR5kiTd7HDAF7i+bc/Fq1/7HyRJelaSpChJkqKys7P//+v2z4Bkj9B8LVvQwY4tCHVqw64rf1FYIf+Kx8Xalk8jB5JUlM1XMbtlt38zLNQqZjw8gIZ13Hlx8XrOZlwxit87pUWEP7N+foKghl58/Olavvp6E1qt8iU4Zu4PSkvL+eyL9XwxYyNhYT7M/vkJmjY17WSfG4m5kMkryzbSxNeLT0f2Q6UyTpvCT6N3cEGTzxdtH8DRUv7ewbnlWezLXkUz504EODS5a3tCl4zQZ95VG0eTCKYkSdslSYq9yWMI8DPQEIgAMoGvbmbiJl+76W2DEGKOEKK1EKK1p+f/TxaXVK5VCUDl2xEVJ+/+h7rKQJ8nMQgDmzJ/k83m9XSrG8SjDVvya+IRDlyWp570dthbWzHr8WE42Voz/rfVZOQXGcXvneLp4cjMGQ/zyOj2bNx0ivETfyMl5bKpwzJzjxOfkMlz439jx84zjHusE19+Nho319o1Yi0tJ58JC9fg6WjPj48NwdbKONNrdmYksSTlBE82aku7OjUfrXUrhBBsyJiHSlLTz2fcXdsz5D2FKJ6JyBuD0MxFlB+ukR2TCKYQopcQoulNHmuEEJeFEHohhAGYS9X2641cBK4fz14PqH5xnt04UHkgir+QLbvVzcqLrnUe5HThQZKKo2WxeSOvR/SioaM7Lx9eS165cbrfeDk7MPuJYZRX6nh2/kryNLWr646FhZqnn+rKl5+NRqMpZ/ykBSxddhh9LcnwNXPvoNcbWPT7ASa/sIiKSh1fffkw48Z2qnWTc7KLNDw7byUAs58YhoejccQ8u0zDa0fXE+ZSh2nh3RTxcbboKAnFUfTweghnS/e7siXK9wECletPSC7fAeWI8t0I7fZq26pd7wBAkqTri5mGAbE3edoxIFiSpABJkqyA0cDaavtS2SM5TIHK41Be/V/erejiOQwPKx/WXppDpUH+DE5bC0u+aT+Ugooyph9dr0gpy80I8vLgh3FDyMgv4vnfVqPR1r7s1JYtG/DLnCdp3y6Iub/u5sVpS7h4Mc/UYZm5R0hNy2Hy1EXMX7CPbl1D+WX2UzRvJn8D8bulsEzLs/NXkVtSxs/jhuLvYZyyFoMQTDuyllJdBV+3G6rI+MFyfRnrM37By8afDh6DZLCoBlGEEBVIlk3AdhSS2gtReQKhz6qWpVonmMAXkiSdliQpBugOvAggSZKPJEkbAYQQOmASsAU4CywXQsTVyJvtCFAHIopnIIQ8Z18WKksG13uOvIosdl3+UxabN9LY1ZtXm/dgR0YSvyUeU8THzWjVwJeZjwwiITObSQvXUlZR+84LnZ3teO+dYUx/dRCpadk8/dw8lv95xLzaNHNLdDo9i5cc5Lnx88nIKODtN4fw5uuDcXSUd0C8HJSUVzB+/mrOZ+fz/dgHCPfzNprvWWcPcuDyed5u0YdgZ8/bv6AGbL+8lMLKXIb4PodauntBlqw7gGU4lCxAGPKrkj5th4E+E1GyoFq2ap1gCiHGCiHChRDNhBCDhRCZV7+eIYQYcN3zNgohQoQQDYUQH9fUnyRZIDm+BvrzULpUjh8BgIYO4bRw7ca+7DWKdAACeDy4Db18gvk8Zgenci8p4uNmdAsL5JORfYlKvcjUxeup0BknY7c6SJJEn95NmTf3aVq3asCsObuYNGUhScnVu6M0898nPiGT8RMX8Ov8vbRvF8S8X56uNf1gb6SsopKJC9cQeymLGQ8PoH2Q/OeHt+JY9gW+jt3DoPqNGRUYoYiPi6VJHMrZSKR7X/zt77405trum2TdHWHIhbJVCN0FJJULksOLYKje7tP9Nd6rdWsRFfW/jQWEEIj8J6AyDslzK5JKnu2NEl0R3yZMwcXKk+eCPkMtU1r09RSUlzF4668IBGv7PIWrtfKdPa7x17HTvLtyO93DApn5yKBaMRLsZggh2L0nnh9+3EZhURnDhrbi8cc6Y28vf2afmXuH4mItv87fw7r1J3Fzc2DKpN507mTaAer/RnmljkmL1nIoOY3PRvZjUAvjiXqOVsMDW37FzsKK1X2eVCQrVmeo5KfkVynTF/NCyLfYqO/+TFYIA5JUtS4U2l2IyhOgS0Oy7oLQrgWLENTOb5vHe1UHSZKQHF8HUYzQfCebXXsLJwb5Ps2lshQOZitTm+libcsPHR4kW6th2pG1GIx4AzSiTThvDe7BrrPneHnpBip0yrftqwmSJNG9Wxi/zXuWgQMiWLkqisefnMvWbafNrfXuQ/R6Axs2nmLck3NYvyGaYUNb89uvz9R6sZzy+zoOJafx4YN9jCqWOoOBFw6tpqhSy08dhysilgB7sldyWZvGYN/naiyWwlCEMBT8fTYpSaq/j9okm+5ItiORbIcgdGeRrDqjcnqrWvbNK8zrMBS9D6VLkdxXI1nK0ylDCMHitM9JKj7JpOCv8LRRpoZrcfJx3jm+mclNOjG1aVdFfNzS98FoPlm36+pKcyBWFvInAsjJ2fgMvv9xG/HxmYSF+jD++R40bVK7auvMKMOpUxf4afYOkpIu07RJPSZP6kVwkPHOAGuCtlLH5Ksry/eH9WZ4m6ZG9f9p9A5+STjMl5EP8GBAM0V8ZJad56ekVwl36cBD9V+skQ1hKEHkPwlqbxA6sGiEynFK1fdEBVX5oVefK/RIV3f8qjNA2iyY1yEMBYjsPmARjOT2+10VuF5PcWU+3ya+gId1XZ5p+IkiW7NCCF47up4VqTHM6jSC3r7GvVteeugUH63dSaeQBnw75gFsLGu3aBoMgm3bY/ll3h5yczV07RLKU090oV49001CMKMcaWk5/DJvDwcOJlHH04lnnu5Gj+5hsn3GlaKkvIJJC9dy7Hw6Hz7Yh2Gt776AvzqsuxDH1EOrGRPUivdb9VPEh85Qyc/Jr6HRFfBCyLfYWTjWyI6h8A2Q7JEcp4PuHKJwGlg0ROXy/81phHYrWIQgWTT4+2vVEUzzlux1SCoXJMdpUHkMtNWuUrkljpauDPZ9lvTSJPZlr5LN7vVIksQHrfoR7lqXaYfXkliYffsXycjD7ZvzwYO9OZCUyvO/raKkvMKo/quLSiXRt084C+c/y2NjO3LkaAqPPzWXr7/ZTHZ27WrMYKbmZGUV8OVXG3nq2V85GZ3Gk493YcH8Z+jZo3GtF8vCMi3PzlvJ8dSLfDayn9HFMi4/i+lH19Paw483I3or5mfXlT/J0qYy1Pf5GoslgGTZBMkiBElSI1kGo/JYC4ZcDPmTgapVJQYNqFxq7sO8wvwnQhgQeQ+BPgPJYzOSykk2/8vSZnCm6CjPB32Gj60yg2YzS4sYum0edmpLVvZ+wqhJQAAbouN5/c/NhNatw+wnhuFqXzsmOdyOvPwSfl98gPUbopEkiUEDIxg9qh2eHjX/AJsxHVmXC1m67DCbNp9CkiSGDG7Jow+3x9nZuJ+HmpJdpOHZ+as4n53PjIcH0KtJkHH9l2kYtn0+QgjW9HkSDxsHRfxcKElgTsqbtHDtynC/yTWyITQ/g1Vb0KUitKuRXL5HUjlXfU8YEIUvI9kOR7Lu+I+t2GuYt2RvwZ0IJoCojEPkDge70aic3pPNf6mumO8SX8RGbcfE4C+xVClzeH4i5yKP7vqdFu6+/Nb1EazUxs1e3X32HC8tWY+PqxNznngQH1f5bjqUJiurgEWLD7Jl62nUahX9+zVj1Mi21K1b87tSM8bj4sU8li0/wtZtpwHo37cZjz7SgTp17p33YFpOAc/NX0mOppTvxjxAh2DjlY4AlOt1PLrrd+ILrrCsx1iauikzGLtcX8YPSS9hEAYmh8ysUaKP0PyM0G5Fcv8DSbLCUDwTtOuR3BYhqavaixuKv0ZSeyPZPXxTG2bBvAV3KpgAhqKPoXQhkttyJKvmssWQXBzN/PMf0Na9P4N9n5HN7o2sTj3NtCNrGRnQnE/bDDT69tPx1EtMWrAGa0sLZj0xjNC6yhQ5K0VmZgFL/zjMlq2n0esNdO0SykMjImnUSJmLh5m748yZSyz/6yj79idgYaFmQP/mPDyq3T0llACn07OYsGA1Avhp3FCaGbEpAVR18nnx8GrWXzjDTx2H07eecmPCVqT/wMn83Tzd8AMa2N/xdEbgan2lIadq9ej0IZJFfUTl2apWp4XTq3YIHSaCZIXQfIfkMBnJpu9NbZkF8xZURzCFQYPIGQAqZyT3lUiSfE2NN2bM50DOOsb4TyfM+WatcuXhm9g9fB+3n2nh3ZjQ2Dgjf64nKSuH539bRbG2gpmPDKRTSAOjx3C3ZOcUs2LlMdZviKa0tILw8HoMH9aajh1Cal1v0fsNnU7P3n0JrFwVxZmzGTg4WPPAoBYMH9YaNzdlthCVZNfZFF5ZuhF3BztmP/EgDTyN0+7uer46vZufzhzglWbdeT6sg2J+Ygr288eFmXSrM4Le3o/UyIYQAlH0LpLTxIOh1AAAIABJREFUm1AZjyh6Cywag8oZKo6AdTcw5CNZBCHZP3ZLO2bBvAXVEUwAod2OKJiA5PAiksN42eLQGSqZlTydgspsJgfPxNnKQzbb1yOu9n1ckxbLzLZDGNLAuOnoAFmFxYz/bTUpV3J5a0gPHopUJi1daUpKytm46RSr1hwnK6sQDw9HBg5ozoD+zc3nnEbm8pVCNmw8xcZNp8jLK8HXx5VhQ1vRv18zbG2tbm+gliGE4PeDJ/liw17CfOrw07ghRmukfj1/pJzkjaiNPBQYwSetByi2K5VXnsUPSS/jZePH0w0/uquqAUPhu6BPBbUPkt1jYBEMlXEI7Tok++eR1Le/tpoF8xZUVzABDAUvgHY7kscaJAv5Dt5zyjP4MellfGwDeTLwfUVKTaDqPOKJvcs4kZPOr11G09ErQBE//0ZJeQXTlmxgX2IqYzu24JUBXVCr7s3VmV5v4NDhZNauO0nU8fOoVBKRkYH079uMdm2DsLSsnd2O7nUqKnQcPJTM5i0xHIs6B0DbyIY8MKgFbSMbGm0GpNxU6vV8um43fxyJoWfjhnw2qj92RhrRdT27MpJ4bv+fdPQKYE7nh7BUKfM+1hkqmZvyFjkVGUwK/gpXqzp3bdNQ9Dlo1yG5zkKybIoQOkT+U0iOLyNZht/29WbBvAU1EUyhz6namrUIQHJb8j8ZVndDdP4e/kz/lq51htPH+1HZ7N5IUYWWUTsXklFSyOLuYxQ7xP83dHoDX27cy+8HT9Ix2J8vHx6As23ta2xdHS5l5LN5cwybt5wmN0+Ds7Mtixc+j53d7ZO5iou1zP11N+XllXh7OdOndzi+vsbfgqvNGAyC06fT2b4zjj1749FoyvH0dKR/32b06xuOt/e9nYiVX1LGS0s2cPRcOk91bc3UPp1MIvwnci4ydvdigpw8WNJ9LPaWyq3SN2TM42DOeh7xf5Umzu1ksSn0uYjiL0B3GsnpfYR2G+gzULn+cEevNwvmLaiJYAKIsrVVh8uOryHZPyVrTKsu/kRU3nYea/AmjZxayWr7erJKixi5YwFavY7lPR8jwPHuZszVlD+PnuajtTvxcXHi+7GDCfIyTRxyotcbiDp+nsTELMaOubOz4itXiog+lYZarSIl5Qp5+SW8Mm0AeXkavvxqE3l5Gpo09uXFqcoUi9dW9HoDsXEX2bcvgT17E8jN02BjY0mnjiH07tWUli38/xNnx/GZ2UxZtJbs4hLeH9aLwS2rl/QiFwkFV3h41yJcrGxZ3vMxxcpHAOIKD7Mk7Qvauw9kkK+811EAUbYaoUsFKpAcpv6js8+/YRbMW1BjwRQCUTAByvcheayWdWu20lDOrOTXKazMYULwl7hZeclm+0bOF+fy0I6F2KotWdbzMXzsTJNBeCL1ElMXr6e0opKPhvemX7Pa28NTKYQQf58RlZSU8+r0P5gyqTdr1p0gLNSHtpENWbBoP507NaJd24b/89p9+xNZtToKXx9XHhvb6Z7LBr0eTYmW48dTOXw4mcNHUygsLMPSUk3byIZ06xpKh/bB2NgYf5tSKdaeOMP7q3fgZGvNd2MGG3U81/Vc0OQzasdCAJb3HIefg3Ir9mztJX5OfhVP63o80/AjLFS15+9pFsxbUFPBBBD6bETOQLDwQ3L7A0mGOW3XyC3P4qekl3G18uK5oE8Uq88EiM3L5NHdi/G0sWdZj7GK3lH+G5cLNby0ZD3RFzJ5rGNLXurfCUsj14uaGoNBoFJJxJxOZ83aE7SNbMjGTaf4ZmbV9vyOnXEcPJTM228O+fu5UFVC8c33W5kysTdRJ86Tn1/Kiy/cPGW+NqLT6YlPyOTkyTSiTpwnLu4SBoPA0dGGyDaBdOwQQmSbgDva2r6XKK/U8cXGvSw7fIo2AfWY8fAAkyT3QFWDk9E7F6KprGBJ9zE0crn7s8RbUa4vY1bydDS6QiYGf4mLVe0qMauOYNbuhp+1CEntCU7vIQqnQskscJgkm213a29G1H+B31M/Zc2l2QyvN1mxDLWmbnX5tfMoHt+zlLG7l7C4+xjcjNwNCMDL2YH5z4zky417WXjgBKcuZDLj4QH3VJODu0GvN1zdjr3MXyuOEdkmEEtLNXZ2/7+NVFGhp7S0qsWgwWBApVJTUFDK8ROpdOwQTNOm9bC2sWD2nF1UVOiwsqqdH+eSknLiEzKJjbtIbOxF4s5cQqutRJKgYUMvRj/UjsjIQJo09v1PbLfeiuVHY1h2+BRPdG7F1L6dsDDRz5pdpuGx3UsoKC9jUfdHFRVLIQQrL/5AdvklHg94u9aJZXWpnZ+wWopkOwBRvgOh+RGsOsva0CDMqQ09vEax8/If+NgG0sFjkGy2b6S1px+zO4/kmX3LGbd7CYu6PYqLtfFb2FlZqHlzcHdaB/jyzoptDP/udz4Y3pveTYONHosxEUKgVqs4duwcK1ZF0Szcj0EDI/jx5+34Xdf8PT09Fy8vp6uvqfpabm4xGo2Wli0bAKDXCwICPElKvkyTxr7/1955h8dVXH34ne1NvcuWrOreKwZsjMHEGELoLWBCCQHSSEJCEggQAiEkkAD5CISEkFBNNRA6uIJtcMO9SVa3ulZarbbv3vn+2LVjjIVloy2S7+tHj3f3zt45s7f87sycOSfWTfkSXV1uqqpbqapuo6KimT0VLdTVtSMlCAHFxVmcOX88E8YXMGHCMFKSB0boxP7gshMmMiIvi+klBXGzod3r4srlz9Hs6eap2ZcxPj0/qvWtbHuNbY41zM9dSFlS/90v44UqmEeJSL4T6V+PdPwcMhYjNP03pHJq9kU0eap5t/HfZBsLonqCnZRTzGMnXcgNn7zMwhXP8/Qpl8dFNAG+MW44o/Kz+fmid7j5ube4aPo4fnHWKXFxr48FQgiWr9jF6jUVXHrJDCZOCIc+8/mCFBT8TzCbmh1MnFgI/C9zfE+PD0XKAzFR3W4fQgj0MUreLaWk2+mltdVBU5ODxqYu9u2zU19vp66+g64u94GyGek2yofnMHfOKEaOyGPU6Hxs1oHtGf110Gk1cRfLK5Y9R72riydnX8rUrOjasqt7PR82P8/41FmcnPWtqNYVK1TBPEqEJhlS/4S0X4l03otI+X2/7VsjNFxU8GMer/wli+oe5IayP5BpjN4T4Cl5pTx28oXc+MkrLFz+HP+Zc3nMg7XvpzAjlWe+dwl//XA1T328nnVVDdx38fyYhwaLBe3tTv7y8HsYDDrS061UVLQw6+ThTJ40jM1b6gmFFHbtbkJKydhIr3H/cKvFasDnCx5Y79ne3oNeryU5+chCtH8oVKsVB4b8pZSEQpJAIITfH8TvD+J2+3G7ffT0+HA6PXQ53HR1uemw99DR0YPPF/zCflNTLQzJT+PEE8ooLMygpCSbkpJs0tPiMz+n8mXavT1csex56l2d/GPWJZyQHd34tC3eOl6s+zN55mLOG3pTwmeG6Suq088xojj/Aq7HECl/QZjP6pd97sfua+axyluxaJO4oewPmHXRdcxZ0bSXGz55meKkDJ6eczmZpvje6D7bW8+vX36PNqeL606Zzg1zZ2CIUQ8qFkgp2bevkw57D7W1HTTsszNtSjHTppVw3/3/ZeeuJkwmPTd891QmTy6ix+Wlvs5OWVkOer2W665/kt/c9i2GDcvkl79+iTmnjGTe6WOPOP/3vZueoqKipc92arUakpJMpKRYSE0xk5GRREa6lazsZLKzksjLSyUvNxWb7fjtNQ4Emt3dXLn8eZrc3fxj1sXMzCmKan09wS4er/glAennprI/Ri2SWX+hesn2Qn8KppQBpP0KCFYgMl5H6Ar7Zb/7qXHt4F9VdzHMOoqrim6Puhv2qpZqvvfxy+RZknl6zuXkxWnJyX66PV7+8NYK3ti4g+G5mdx74RmMHhK9JTeJhMfjp9vpISc7nKKoucXB+x9s5YrLT0Sr1fDue5t587+fk5RkxmIxcMtPz+yTaO2tasXl8hEKKSiKRIjw8LBWq0Gn1WA06jAa9ZjNBiwWAyaTftD0DI5X6nu6WLj8Oew+N/+cfQnTsvr3PnUoAcXPv6rupNFTzXdLf8dQS+L7I6iC2Qv9KZgAMrQP2f4t0BYiMhb1eaFsX/m8czmv1D/C5LRTOX/oD6J+81rfVs+1H79Iit7E03Mupygp/chfijJLd+zl7teXYHe5uXrWVG487QRM+uN7JkFRJLV17bS0dFNelkNGxsALND6Qsfe4eXTJp1Q0t3PO5FFcOO3I4dfiQYWjje+seAFPKMBTsy9lQkZ0ncIUqfBS3Z/Z6ljNpYW3MC41esHb+5OjEczB68MdA4R2CCLlPghuQzrv7/f9T0qbw9ycS9jYuYxlrS/3+/4PZWpWAc/O+TbuoJ9Llj7Njs7mqNd5JOaOLuWNnyzknEmj+eeKdZz/8DN8WlkXb7PiikYjKC7K4oQZpapYxoGX121FSsnvLpjHGxt38Oyqz1GUxOp4bO7Yx2VLnyEkFV449cqoiyXAh83PsdWxmvm5CweMWB4tqmB+TYRpHli+A/61SMV9xPJHy9zsi5mUdipLWhax3r6k3/d/KOPS81h02kJ0QsNly55lTUtN1Os8EilmE/dceAb/vPZ8FCm59slX+cWid2lzuuJtmspxxP7RuJq2TsYX5DIsM40b557A9n0tbN/X97nhaLOiaS9XLH+OJL2RF0+7KqrrLPezpv0dVrYtZnrGN6LiESu9HyCDlf2+36NFFcx+QCTdgsh4CaHpfw9TIQTnDb2RcttE3mh4jF3d/Tek3BtlyZm8fPp3yDMncc3KRbxVtyPqdfaFmWXDeP3mhdwwdwYfbKvg7Af/zTOrNhIIheJtmsogYkN1Aw+/v4q1VfUHPtsfyrDb4yU72YY5suRpZlkhFqOBypYO/MH4n4evVW/h+o9fYpgtjRdPW8gwW/QD+m/rWs3bjU8yKnk638y/rt+njmRgJ7LrFqTzgX7d77GgCmY/IIQBIaK3hlErdFw27OfkmotZVPsAta6dUatrP/mWZBbNXcj49Hx+vGYxT+xaQyLMd5v0On4470TeuPlKJhTm8Ye3VnD+I8/yyZ6aeJumMoAJKQoA72/dw12LlxCSCi+v3cpzqzcBHBCBZLMJrUZDs6OHLrcXIQQlWelUt9sJRvYRD6SU/HX7x/x87X+ZllXIC3MXkm2Ofp7Wvc4tvFT/EAWW4VxS+BM0/ZymUCoOZNcPQZOMSL6nX/d9LKiCOUAwas18p/h2UvSZPF3ze5o9NVGvM9Vo5uk5l7OgYBT3b17KHRveI6DE/ykaYFhmGn+/+jz+euU5BIIhvvfUYm54ajEVze3xNk1lgODy+Xlp7RZ+/Ox/eXb1JhweLxtr9vHrc+bw0/mzuPKkySzbuZcdkeHW/SMZY4Zk09jpoLrNDsC4glw+3l0Tt0Ab/lCIW9e+xUPbVnLusHH8a/alJOmjH4e3wV3Js7XhteILi27r9xjYUoaQXT+DUBMi9ZE+JYOONqpgDiCsuhS+U3IHRo2Jp6rvpt3XGPU6jVodD888j+tHzuT5vRu5buWLdPu9Ua+3LwghmDu6lDd/spBbzpzFpromzn/kWe549UNaHD3xNk8lgenx+rj6H6+wvmofF00fx8pdVayuqGVnYxsdzrAvwviCXEYPyWbxhi9OSUwvLSAr2cbTn2wEwBsIMCo/G18g+KV6oo3d5+aqFc/zas0WfjRmFg/M+CaGGCQxaPHW8u/qu8P3pOI7orJWXPY8DP6ViOTbEYbJ/b7/Y0FdVjIAafM28MTe29FrDHy39J5+yVreF16u2sTt699lmC2Nv8+6KG45NXujy+Xh8WWf8cKnm9EKwWUzJ3LdKdNIsx4/8UpV+o7T6yPJFO4V/X3ZZySZjOi0GpbvrOJvV50LwNb6Zu59cxmLvn/ZF77rD4b4w1vLqWzpoMHu4Lfnz2PWiKKY2r/H0cb3PnmZZnc3908/m3OGjY1JvR2+Jp7YexsCwfWl95Ju7P9oXNLzTjjRhfkiRPI9UV1Sp67D7IXBIpgAjZ4qnqy6E4vWxnWl95Cij414fdZay/dXvUpISh6eeS6z80qP/KUY02B38OhHa3hr0y5Meh1XnDiJq2ZNIdWiRqRR+SJOr49731jKmr11XDhtHOdMGs1N/3mdF79/GTaTkX2dDv7y3ipumDuDspwMttY34wsGmVo8FJfPT6fLw9D0lJjbvWTfHn766RuYdXr+dtKFTM4cGpN6O/2t/GPv7QQUH9eV/o4cU/8HQpCB7ciOy0A/GpH+dL+vbz8UdR3mcUC+uYTvFN+BK9jNv/beSXfAHpN6Z2QP4/UzriHfksy1H7/I33euTghnoIMZmp7CfRfP5/Wbr2T2iGKeWL6Weff/kz+/9zEdPf2/9Edl4JJkMjKhMJ/nb7yUjh43qytq0WgEL3y6GYBujw+TXkdhRio9Xh+t3T3YIr1Sq9EQc7FUpOSRbSu5/pOXKUpKZ/G8a2Imll3+Np7cewd+xcvVJXdFRyxDrcjOG0GThkj9v6iL5dGi9jAHOLWunfy7+nck6zO4tuS3JOtjE53HHfTzy7Vv83b9DuYPHckfpp8dE0eDY2FPcztPLFvLe1t3Y9BqOX/qWK6ePYUhabHvGagkLjsbW3lt/XZKs9PZsa8Vp9dHTXsnJw8v4mdnzoq3eTj8Hn7+2X9Z0ljBeUXjuGfKmZh0sXE06vK38c+qO/AEnVxdchdDLWX9XoeUnki40b2I9OcR+tH9XsfhUIdkeyGRBHP/uq7+oMa1g+dq/shlw26hxBabeQwIt+Gfuz/jT1uWUmhL49ETL4jJIuljpbrNzr9WrufNz3eiKJIzxpZz1awpgzIjisrR09jZzZ2LP+KByxZg1ut4Y+NOxhfkMiIv/kmPt9mb+MHq12hyd3PbpNO5smxqzOL8dvpbebLqTtxBJ1eX3ElBFOLDSqkgu34Mvg8QqY8iTKf3ex29oQpmLySWYCoI0X8j4r6QB6M2Ps4ta1vr+NGa13AGfPx28nwuKB6f0EG7Wxw9PLv6c15euxWn18eEgjyuOGkSp48pG1RZUVSOTLfHy6d763l70y6q2uxcPH0cl50wEd0RMr/ECiklz+/dyD2ff0i60cJfTzw/ZkOwEM6c9GTVHXgVD1cX3xG1YOpK9/3gfhKR9CuE9eqo1NEbqmD2QiIIplR6wP0UUukExY5I+gVCG92s57GgzdPDTz59gzWtNZw7bCy/nTIfW4IO0e7H5fPz+obtPLt6E3UdXWTYLFwwbSwXTRtHflp8s7WoxIZgSOGltVsw6/WcNXFkQj0wdfu9/Hrd27zbsIvZuSU8MOMcMmKYeq/N28CTVXcRlH6uLr6TIZboOPhJ1zNI5+/A8m1E0h0xf9hWBbMX4i2YUulCOn4D2iyE+VLwLUF6XkOkPYbQ9f+cQKwJKQp/27mKR7Z/TIE1lYdmnsv49MR/GFAUyaqKGl5Ys5mVe6oBOKm8iAumjWXOyJKEuomqHBl/MIjD4yMraeAmsN7Q3sBP1rxOi8fJT8edwndHzkQTQyFp9FTz76rfghBcU3wXueboJJyW3g/CkXyMcyNOPrG/1lTB7IV4C6bifAB8qxC2HyFMpwIgg7UgrCAsIDQIMfCXPqxrq+PmNa/T7nVx89jZXD9yJlpNYgxxHYnGzm5eXb+Nxeu309LdQ6rFxIIJIzln0ijGDs1J6KHm4xkpJZvrmnjz8528u2U3J5UP44HL+jexeywIKCEe3fEJj+5YxRBLCg/NPJeJMcg0cjA1rp08U30vRq2Fa0ruItMYnYde6V+HtF8N+lGR5SPxmVJSBbMX4imYMrAdab8CYb0RGWoEpRGR+jhIN9L1JIQaIbgdYfspwjQ3Ljb2Jw6/h9+sf4+363cwNbOAP834JoUxCATdX4QUhdUVtbyxcQdLduzFHwwxLCOVBRNGMH/8CMpyEitow/GIlJKKlg7e3bKbdzfvpt7uwKTXcdroMs6fNoYTSqObLLm/qeru4JbP3mSzvZHzisZx5+RvxNzzfFf3el6ofYBUfSZXl9xJqiE6Dk8ysAtp/zZoMhEZLyA08cu9O2AFUwjxIjAi8jYV6JJSTjxMuRrACYSAYF8bG0/BVLp+jNCNQthuiHiE/QiR+mek41YQFoT1Ggg1I3v+gkh7Iq4nUH8hpeT12m3ctfF9FKnwqwmncVnp5AHXS+v2ePlwWyVvbdrFuup6pITS7HTmjS3n9DFljMzLGnBtGqhIKdnR2MpH2yr5cHsF1W2daIRgRmkBZ00cybwxZQfWSQ4UFCn5T8U6/rRlGWatnrunzOeswtgsqTiYDfYlvN7wGLnmYr5TfDtWXXSWXclgHdJ+GSAQGS8itLHtQR/KgBXMgxFCPAg4pJR3H2ZbDTBVSnlUkbbj2sPseRSMZyD05chgNdLzSrhXGdiGJuvDcBnFhXTeh7D9EKHNia49UlLv3kOhdcSRC39NGt3d/HLtW6xqqeaknGJ+P20BQ62pUa83GrR19/BB5Ga9oXofipTkpyZz6qgSZo8sZlrxUIx6XbzNHFR4A0HW7q1nxe5qlu+sotnhRKsRTC0eyhljy5k3tpwMW/+n1osFNU47v1r3Nmvb6jg1r4zfT1sQkywjByOlZHnrq3zU8jxltglcPuwXUfO4l6GWsFgqPYiM5xPCd2PAC6YIP67XAXOllBWH2V7DQBNM9wtI19MI8wKkVMC/FkJViLQnDyzQlb7PkD1/QqT9G6Hp/2DGB7OkeRHLW19hRPJUTs46hyJrdJ9opZS8sPdz/rB5CRLJLeNO5YqyKQNmbvNwdPS4Wb6ziiU7Kvm0sg5fMIRJr2N6SQEnlhcys2wYpdnpau/zKNk/1Lqmso5Ve2pYX92ALxjCrNcxs3wYc0eXMmdkyYCOERxUFJ7as5a/bFuBQaPl9knzuKAoPsuxFKnwQu2fMGhMnDf0JnSa6ARDkIod2fFtUJrD9zjDhKjUc7QMBsGcDfy5t0YIIaqBTkACf5dSPtGX/cbb6Uf6NyO9byKMs5H+zwHQJN18YLvSdjrC+j2E5SKkDEXNY8yv+His4hdcOuxntHrr+ahlEafnXMq41JOiUt/BNLoc3L7hXVY07WVSxhDunbogoYMd9JX9vaBP9tTw8Z4a6jq6AMhMsjC9pICpxUOYUjSEkqwMNBpVQA9GUSQVLe1sqNnHhup9rKtuOBDCsDgrjZOHF3Hy8KJB03vfZm/itvXvsK2zmXlDhvPbKfPJiXGv8lCCSgCt0EVNsKXiQNqvikTxeRJhmB6Veo6FhBZMIcRHwOFCq9wmpXwjUuYxoFJK+WAv+8iXUjYKIbKBD4EfSilX9lL2euB6gMLCwim1tbX90YyvjfStRHqXoEn5LVJKZPdtoHSiSXssvP2gSEDSvwECmwEdwrrwa9e9tOUlNneu5Ccj/+8Ln4dkkE2dKyi0jCTLFL15BSklb9Ru495NH9Ht93L1iOn8aMwsLLrEihv5ddjX6WB1RR1rq+pZV9VAm9MFQLLJyPjCPCYU5DKuII+xQ3MGdE/pWOjocbO9oYUt9U1srm9mS10TPT4/ADnJNqaXDGV6aQEzy4aRlxpfIelPnAEfD21dwdOV68kwWrhj8jc4c+jIQT8CIRUnsvM7ENgVXkJnnB1vk75AQgvmkRBC6IB9wBQpZUMfyt8F9EgpHzhS2Xj3MA9GBnYgHbeAbjRoUiBYi0h7FCGMSBlACD1S6QLfcqTrKYT5AqT3LdBPQST9/GtFCaru2c5nHe/RFWhlft5VFFlHs7VrNZU9m/CGXLR46xifOou5ORf3Y4u/TKfPzR83L+Wl6s3kWZL5zaR5nDFkxKC7gUgpqbc72FCzj021jWyqa2Jvawf7L7281CRG5mUxIi+L4bmZlGZnUJiROuDXf/qDIeo6Oqlo6WBPczu7m9rY3dRGcyRXqUYIynIymDQsnwmFeUwpGsKQtORBefzfqt/B7z//iDZvD5eXTuaW8aeSbBj4S8iOhFR6kJ3XQmBreJ1lAq4AGOiCOR/4lZTylF62WwGNlNIZef0hcLeU8r0j7TuRBBPCTj64nwbDiaDNR2izvhAyT7pfQwZ3IQxTEKZvIEMdyO5fIlIeQmiOflG2IhU0Bwntmva38YbcnJpzEQ/uuokz865idMoM6ly72dL1MWcPua5fY972xvq2eu7Y8B67Ha2clFPMHZPPoCw5/tnVo4nL52dbQws79rWwfV8ru5vbqGnrRIlcjzqNhoKMFIZlpjEsI5WC9FSGpieTl5pMfloyFkNsgm4fCZfPT1NXN42dTho6HdR3OKjt6KS2vYt6exchJdwerUZQnJXOiNwsRg/JZsyQHEYPycZqHDyjCodjV1cLd2/8gM/a6hiTlsvvpsxnQozXVcaLL4rlXxCmb8TbpMNyNIKZiBMClwIvHPyBECIf+KeUcgGQAyyO3MR1wPN9EctERGisYLsRACkDyGAdQhdeOyYDO5DBCoSu/H8nmncxaLKPSSwB7P5mbLpUTNqwR2FIBhFC8GHz86TqMxmdMgMAmy4Fu78FV9ARNdfyg5maVcCbZ1zLc5Ub+Mu2FSx47wmuKJvKj8bMItU4OIcrrUYDM0oLmFFacOAzXyBIVZudypYOqlrtVLXZqevoYk1FLb5g6AvfTzYZyU6xkWmzkGGzkmY1k24zk2I2kWQykmQyYjXqMRv0mPR6THodeq0GnVaLRiPQCBGeCiA8hxgMhfCHQvgCIbyBAG5/AJfPT4/XT7fHh8PjpdPlxu7y0NHjpt3porXbhdPr+4JdZr2OgoxUynMz+Ma44ZRkpVGWm0lxZtqgmH/sKx1eFw9tW8miqs9J1pu4Z+qZXFw8cUA7uR0N4WHYayGwLaHF8mhJuDNYSvmdw3zWCCyIvK4CEsO9ql/RgPc9pK4YYZoHShdIBxjDaYVkYAcy1I4wzDjmGiqdm1nd/hazss4l21RAs7eWbGMB6+0fcU3JnQfKbexchlajdtveAAAgAElEQVTosOpSvtTD9CtedMLwhZ5qf6DTaLhq+DTOLhzNQ9tW8kzlehbXbOUHY07mirIpGLUJd6r2O0a9jlH52YzK/6ITlKJI2ntc1NsdNHU5aerqpsXRQ5vTRbvTxea6RjrdXlyRecBoYTUaSLeayUiyUJyVzozSQrKTreRHer1D01PItFkG3ZDq0eALBfn3nrX8bedqPEE/V5RN4cdjZsf8wc8V7MaoMaPT6GMySnQwUulC2q+B4G5E6kMI0xkxqzvaJNyQbDRJtCHZr0LpvgehSUHYfohU7OB+ESm9CPN5CF3RMe+32VPLkpZFaISWEUmTAah2beeCgh8CEFB8/HHn9QeyqYdkCG3EW7e6Zztr7R/Q5KliUtqpnJJ9/tduZ2/s7mrlvs1L+Li5igJrKj8dN4ezC0fHNJ7mQGN/DNVujxeXL4DL58PjD+L2BwgEQ/hDQYIhSUhRUCI3UQFoNRp0WoFBq0Ov02Ix6DEbdFiNRmxGA8lmI8lm04CfU40mIUXhjdpt/GXbChrd3ZyWX86tE+ZSGuOphXZfI6/UP4JW6Mgw5HHu0Bv7/eH2q5ChDmTn1WFv2NT/OxACNJEZ0HOY0WQgCOb+p0HpfgnpW4pIuR/Z/VvQ5CCMsxHGmf1SjzfkxqS14PC3817zM1xS+BNCMsi7jf+hJ9jFpcN+hiJDaCJiudOxls+7ljMyaSojkqfwWv2jzMu9nFxzUb/Y0xsrm/byxy1L2dnVyqjUbH42bg5z8sqO616MSuIgpeSjxj08uGUFFd1tjE3L5dYJp3FiTlFcbFna+hJ6YWB29nk8V3M/eeZiJqTOIsOYF/36Q83hpSOhJkTa3xDGk6NeZ38w0Ocwj2v2C4GwXBzxpP01aFIRtu/3azADk9aClBK9xogv5OGxilvJNOaj0+g5K/8aYL+TkJZWbz117t0UW8cwOT3s5dYd7MQd6uk3e3pjdl4pJ+eW8N/a7Ty0bQXXffwSkzOGcvO42ZyYXaQKp0pckFKysrmKh7atYIu9ieKkdB6ZeR5nFoyKySjIocOs+9+3eGopSwrPWJ2Wcymfdy6jqmdb1AVTBmvCgdRlV2Sd5bSo1hcvVMFMYDQpd4U9aYW5X5NN70cIgUWXxMLiX7PHuRGBhhLbuANDsPsjfjS4K1GkQqltQuR9BUPNZSTpYhPeTiME3yoay5kFo3ilehOP7ljFwuXPMzWzgB+OOZmTcopV4VSJCVJKVjTv5a/bPmaTvZGh1hTum3YW5xeNRxcjh56gEiAo/Zi01gM2CSFQZIgi22g8kQfZXPMwMtx5dPpb6PS3kmaIToAQGdiB7LwGpESkP4PQj41KPYmAKpgJzrF6xB4twyPzmQAOfzubulYyJX0uNl0qzqAdiy6JbFM403u9ew9mnQ2dJrZLAgxaLZeXTeGC4gm8VLWJx3eu5qoVLzAhPZ+bRp/E3PxydY5TJSqEFIUP9+3hbztXsb2zmSGWFO6ZeiYXFE3AoI3+3K4iFUIywJKWF9npWEuRbTTlSZMYmzLzwMOiRmix6VLZ566k0VNNvrmYPHMJDe7KqNklfWuQXTeBSEZkPIXQlUStrkRAFUyVL5FiyGSIuQRbpAe5t2crJ2WeE37t3EKnv5Uh5tKoPbEeCaNWx5XlU7m4ZCKvVm/miV2f8r1PXqY8OZPvjpzJNwvHxOQmpjL48YWCvF6zlX/s/pRqp50iWzr3TTuLc4eNi9k55gx0kqRPo8XbSJOnhmtL76bFW8eylpewaG2U2MYRkkG0QscQcxnN3lr29mwm31xMgaWcV+ofIaD0vwe19LyDdPwcdEXhmNjawwVwG1yogqlyWMqSwlnVQjJEmW08GzuXYtHZeLvpKU7IOJNS2/g4WxgWzsvLpnBxySTertvB33et4Rdr/8uDW5exsHwal5RMJM04MLNYqMSXDq+L5/du5JmKDXT4XIxJy+WRmecxf+jImK2lrHfvYVXbf+nwN3F96e9pcFcy1FJGsj6dZH067b5GPmx+nu+V3YcgbFOGMZfhSZP5sPk5TBoreo2BDEPegbXX/YGUEtz/QjrvD0ceS3scoYn+eu1EQPWSVTkiilR4r+k/uENOCiwjmJGRmIuQpZR83FzFk7s/45OWakxaHecOG8fC8qmDIsC7SvTZ0dnM0xXreaN2G34lxCl5pVw7YkbMHczebnyS7Y7PmJd7GRNSZ6MRWnY41rKi9VVuLL//QLn7dlzDwqLbGGIp/cL3a1w72e5YQ4u3jrk5l1BkHdUvdkkZQjp/D+5nwDgfkfonhBhY+UcPRfWSVelXNELDgvyrvxRaL9EQQjA7r5TZeaXs7mrl3xXrWFy7lUVVnzM9q5DLSifzjaEjjosgCCp9xxcK8m79Tp6r3MjGjgbMWj0XFk/gquHT4haiMcc0jBZvPZPSwusYewJdjE6ZzjuN/2Jvz1ZKbeMAmJp+Ohs7lzLEUkpA8bG1axWT0+dSZB1FgaUcrei/c10qPUjHT8G3HCxXI5JujYozYiKj9jBVBjWdPjcvV2/mhcqN1Lm6SDdaOL9oPJeUTKQkOSPe5qnEkT2ONl6q2sTimq10+T0U2dL5dtlkLigeT4oh/iEZH979Y0pt42nyVmPW2hidPJ023z6avbVcVXw7ABvsS3AFHczOPh+Hv529PVsYl3oyOqHv1x6xDDUhO78HwQpE8m8Qlsv7bd/xRg1c0AuDWTClDCAdtyGsCwe1W/exokSGaxft/ZwljXsIScmkjCFcWDyBswpGkXQcZI5QgS6fh3fqd/BK9RY22xvRazTMGzKCS0snJdy63k/b32Vn9zrm5V6GUWNhRdur5JqK2NW9nlLbeIZYSlje8gonZC5gfGr0ggRI/6awJ6z0hkPdJVh6rq+LKpi9MKgFM9iAtH8blE5Eyh8Q5gXxNilhafP0sLh2K69Wb6Gyux2jVsdp+eWcO2wss3JLVQ/bQYYvFGR5UyVv1m5naWMFfiXE8JQsLiyewLeGjSXTFJulW8fCfu9XgDXt79AdsDMhdRY1rh1sdaxibMqJzMyM3rUuPYuRjttBm4tI+ztCVxa1uuKFKpi9MJgFE0CG2pFdP4DARrBej7D9BCHic/Nv8daSZRx6ILReIiKlZKu9iddqtvBW3Q46/R5SDCbOGDKCBQWjmJlThF6TuPar9I4/FGJVSzVv1+/gw3176An4yDBa+WbhaM4vHs/o1JyE6k32hY+aFyGA03IvjXpdUgaRzj+C+99gOAGR+jBCkxb1euOBKpi9MNgFE0BKP7L7d+B5EQyzEKkPIjSxicizH3fQyYO7byLdkMM3879LoXVETOs/FgJKiE+aIzfYht30BP2kGEyclj+cM4YO5+ScEsy6xMhBqXJ43EE/HzdX8UHDbpY0VuAM+EjWmzhj6HDOLhzDzOyimEXj6S/8ipdP299lm2MNVl0yZ+VfQ6YxP6oZSKRiR3bdDP5PwbIw4twzeM99VTB74XgQzP1I96KwcGpzwlkD9KNjV7eUbHOs5u3Gp3AG7UxOm8s3cq/Apo+tcB8rvlCQj5ureLd+J0sbK+kOeDFqdZyUU8SpeeWcml9GniU53maqAPtcDpY3VbKksYI1LTX4lRCpBjNz88tZUDCSE3OKB7RXdEiGWNvxPoWWEV9aOhINpH8zsuuHoNgRKXcjzNHLSJQoqILZC8eTYML+yfofhec1k+9EWC6Maf2+kIdlrS+zuv0tdMLA3JyLOSHjzAMxagcCASXE2tY6Pmrcw5J9FexzOwAYkZLNrNwSTs4tZmpmgdr7jBHuoJ+1bXWsaq7m4+YqKrrbASi0pnLakOGcll/OtKzCAdeTjDdSSvC8gOy+N/KQ/VeEfky8zYoJqmD2wvEmmLB/eOUn4F8D5vPDwili6zLf7mvk7cZ/sce5kQxDHvPzFjIqefqAm0OSUlLZ3c6ypkpWNlWxob0evxLCoNEyKWMIJ2QPY0b2MCak52NSBbRf8AQDfN6xj89aa/m0tZbN9n0EFAWDRsu0rEJOySvl1LwyipPSB9z5lChIpQfZfQd43wLDbETqAzGfxoknqmD2wvEomBCJztHzf+D6G+hKESkPI/TlMbdjj3Mj7zb+h1ZfPUXW0czPW0iBZXjM7egv3EE/69vq+aSlmk9ba9nR2YwEDBotY9JymZJZwOTMIUxIzydXHcI9IlJKmjxONnXsY1P7Pja017O9q5mAoqARgjGpuczMKeKknCKmDPBefTTnII/KjsCO8AN1qBZhuznsLHi8BSNQBfPwHK+CuR/pW4V03AKKC5F8G5gvjvlFG5Ih1ts/YknLIlxBB2NTZjIv99tkGvNjakc0cPg9bGhvYG1bHRvaGtjW2YRfCQGQY7YxLj2fsWm5jE3LZWRqDrnmpIS4acaD/eK4s7OZ7Z3NbO1sYqu9iTavCwg/dIxPz2dK5lCmZRUyNXPooFgr2+qt5/3mZxmeNDmuISbD8WCfDceD1aQiUv+MMEyPmz3xRBXMXjjeBRNAhlqRjl+AfzWYzkQk3x2XwMm+kIdP2t/kk7Y3CCp+JqfP5dTsi0g1ZMXclmjhCwXZ2dXC5x372GpvYou9kRqnnf1XXKrBzIiULMpTsihNzqA0OZOSpAxyzEmDJk2ZIiXN7m6qnXYqu9up7G6noruNPY42HH4vAAIoScpgXHo+49PzmJQxhJGpOYNqPazd38LSlpfY1LkCg8bEGbnf5oTMM+Nii1TsSMdt4FsCxlMQKfcjNOlxsSURUAWzF1TBDCOlAq5/IHseBk0mIuVPCOOMuNjSE+hieeurrLW/D8DU9HnMyb6AZP3gvIB7Aj52dbWys6uFnV0tVDja2dPdRk/Ad6CMWaunwJZKoS2NAmsqQ6wp5FuSybMkk2tOIsNojVnGjCMRUhTafS5a3E4a3d00uh3sczlocHVR29NFnasTXyh4oHyS3sjwlCzKk7MYlZrNqLRcRqZkY9XHNrdqrOjyt7O89RU22JegEVpOyJjP7OzzseriM0QvfR8jHb8EpQuR9HOwXHXcjnLsRxXMXlAF84vIwFZk188gVAuWaxBJN8ct80CXvy1yY1mKRmiYmn46s7LOI9UQn+DXsURKSau3h73dHdQ4O6h22qnr6aS2p5MGlwNPKPCF8lohSDdayDRZSTdaSTdaSDWYSDaYSNKbSNIbseoNWHUGjFodJq0evUaDQaNFKzRohSZyk5RICSGpEJIKfiWEPxTCpwTxBgO4ggFcQR89AT/dAS/dfi9dfg92nxu71027z4Xd50Y55B5i0ekZag0L/jBrGsXJ6RTZ0ilLziTTZD0ubtCd/lZWtL7Gxs6lQPwfBKX0IJ0PhLOM6MoQKQ8i9P2TwWSgowpmL6iC+WWk4kY6/wCeRaAbjkj5Y0zXbB6K3dfM8tZX+bxzOUIIJqedyqys88gwDv7ktIdDSond56bJ3U2Tp5sWt5MWbw/tXhcd3rBgdfjcdPu9OPweonU1a4QgRR8W5XSjhQyjhQyTlUyTlRxzEjnmJPIiveA0g/m4EMXD0e5rZEXrq2zqXIkQgilpp3FK9vlxnWqQgS3Irl9AqCoSiOAWhBj488H9hSqYvaAKZu9I3/JwzEjFjrDdCNYb4hrdo9Pfysdtr7PBvoSQDDEu5URmZZ9LvrkkbjYlOoqUuIJ+nAEfnqAfV9CPLxTEGwriDwUJKMqB3qQiJQKBEBzodeo1GgxaHSatDqNWh1VnwKIzhHusOsNxK4J9od5dwcdti9nh+Ayt0DM9Yx4nZ36LlDiOkEjpj3jH/wM02YiU3yOMJ8XNnkRFFcxeUAXzq5FKZzg6kPct0I1CpNwX194mQHfAzur2t1jb8T4+xUOpbTwnZ51DuW2SegNXiSuKVNjj3MgnbW9Q7dqOSWNhRsZ8Tsw6G5suvusYZWBLeK4yWBlef510G0KTFFebEhVVMHtBFcy+Ib0fIrvvBKULrNchbN+Pe1Z1T8jFuo4PWN3+Ns6gnWxjATMzFzAx7RQMGnV4SSV2+EIePu9czpr2t2n3N5Kiz+TEzLOZmn46Jq0lrraF5yofDgdN12QhUn6HMM6Jq02JjiqYvaAKZt+RSldkbvM10BaHL7wEWKcVVAJsdaxiVdt/DyTWnZI2l+kZ84/beU6V2NDua+SzjnfZYF+GT3EzxFzGSZnfZGzqzAMpuOKJ9K0KR+wJ1YP5EkTSL9ReZR9QBbMXVME8esIX4W8g1ADmC8MOAwmwZktKSZ17F2va32a74zMUQpTbJjIt4wxGJk9NiBuYysAnqATY2b2OdfYP2NuzBa3QMTZlJjMzz0qYKFUy1B5+uPW+mVAPtwMFVTB7QRXMY0NKT8R54CkQNkTSrWA+L2FCaHUH7Kyzf8gG+0c4Ah3YdKlMSZvLlPTTyDDmxds8lQFIm7eBDZ1L2WhfiivUTao+i6np85iafhpJ+sTICyllCDwvIZ0PgvSA9bsI241xnz4ZaKiC2QuqYH49ZGB3eG4zsBH0kxDJdyRURoOQDLHHuZH1HR+y27kRicIwyygmpc1hXOqJmLTWeJuoksB4Qi62dn3Cxs5l1Lv3oEHDyORpTE2fR3nShIRKhi79m5Hdv4XgtnCC5+Q7Ebrop/8ajKiC2QuqYH59pFTA8zqy54+gdEbmSm5OiGHag3EEOtjUuYKNncto9+1DJwyMSp7GhLTZlNsmDqgUYyrRI6D42ePcyOaulezu3kBQBsg2FjA5/VQmpp6SML3J/chQO7Lnz+B5JbxUJOlWMJ2teox/DVTB7AVVMPsPqXSHh2ndz4CwImw/BMvlCZeZXUpJg6eSzzuXs7XrE9whJyatlTHJJzAu9SRKbGPV+c7jjKASYG/PFrY6VrPD8Rk+xY1Vl8L4lJOZlDaHfHNJwgmQlH5wP43seRSkH6xXIaw3ITS2eJs24FEFsxdUwex/ZKAC6fw9+FeFHQ6SbgXjqQl3w4H/3Si3dH3Czu61+BQPZq2NUcnTGZNyAqW28eg1gzOm6fGOX/FR6dzMju5P2dm9Dm/IhUljYXTKDMannkyJbTzaBBpy3Y+UEnwfIJ1/glAdGOcgkn6J0KkBPPoLVTB7QRXM6BC+qJeHPfVC1aCfjkj+BUI/Pt6m9UpA8VPh/JxtjjXs6l6PT3Fj0Jgot01kZPJURiRPwaqLfRYXlf6jJ9DFLucGdnWvo9K5iYD0Y9JaGZU8jTEpMxN+aF76NyKdfwz7DOjKw0JpnBVvswYdqmD2giqY0UXKALhfRLr+DxR7OH2Y7WaErjjepn0lQSVAtWsbOxxr2dm9DmfQjkAw1FJGedJkym0TGWopSyinD5UvE5IhGtx7qHBuYo9zI/s8ewFI0WcyMnkao5OnU2wbk/BD8DJYiXT+BXwfhoMP2H4YXtKV4HYPVFTB7AVVMGODVHqQrn+C+6nwfIv5gnC0IG3iL/GQUtLoqWK3cwN7nBtocFcikZi0Vkqt4yixjaPUNo5M45CEHHY+npBS0uZrYG/PVvb2bKGqZxs+xY1AQ4GlnBHJUxieNIU8U9GAOFYy2BB+2PS8DsKMsF4HlqsRmvhGDxrsqILZC6pgxhYZake6/gbuFwEBlssQ1u8itNnxNq3PuINOKns2U+nczN6ezXQF2gGw6VIpto6hyDqaIusosk0Fag80yigyRLO3jlrXDmpcO6l2bccVdACQZsihzDaeMtsESm3jMesGjjOMDDUjex4Hz8uEr5PLEbYbEs7zfLCiCmYvqIIZH2RoX9i7z7MY0EWE87oBJZwQSbXlb6GqZyvVrm1U9WzHGbQDYNRYKLCUU2AZzlBLOUMtZXEPwD3Q6Ql0Ue+poMFdQb17D/XuPfgVLwAp+gyKrWMpto2hxDaOdENOnK09emSoGen6O7hfCn9gvgBhuwmhVUM8xhJVMHtBFcz4IoN14R6n5w3CwnlRRDjz423aMSGlpDPQSq1rJ3Wu3dS5d9PirUOiAJCqzyTfXEqeuTj8ZyoiRZ85IIYHY4mUkq5AG02eGpq81TR5qmn07MUR6ABAg4Yc0zAKrSMptAynyDo6rvklvy4yWI90/QM8rwIynE3EdiNCOyTeph2XJLxgCiEuAu4CRgHTpZTrD9r2K+BaIAT8SEr5/mG+XwwsAtKBjcCVUkr/kepVBTMxCAvn4+G5GgDzt8LCOQgilfhCHho9VezzVNLgrqTJU02HvwkZSe1s1FjIMRWQbSog21hApnEIWcZ8Ug1Zg35INyRDdPnbaPM10O5rpNVbT6uvnlZvPT7FA4BAkGnMJ89cwlBzGUMspeSbSzFoBn64NxnYg3Q9Ad63AU2kR/k9VSjjzEAQzFGAAvwduGW/YAohRgMvANOBfOAjYLiUMnTI918CXpNSLhJCPA5sllI+dqR6VcFMLGSoMeIc9ArgA+NpCOu1CMOUeJvWr/hCHpq9tTR7a2jx1tHiraPV24A71H2gjFboSNNnk27MJc2QQ5o+i1RDFin6TFL0Gdj0aQm5TvBgQjKIM9CFI9COI9BOl7+NrkAbdn8Ldl8znf5WFP53KVt1KWQbh5JjKiTHVEiuqYgcUyFGrTmOrehfpJQQWId0PQm+ZSAsYL4YYb1GHXpNEBJeMA9ULsRyviiYvwKQUt4Xef8+cJeUcs1B3xFAG5ArpQwKIWZGynzjSPWpgpmYyFAH0v0MuJ8D6QD9RIT1ajDOG9Su9K6ggzZfI+2+fXT4mujwN2H3tdDpb8GruL9QViCw6lJI0qVh06Vg1aVg1SVj1iZh0SVh1loxaS0YNRaMGhMGjQm9xoheY0AnDGiEFs0RguUrUiEkgwRlgKDix6/4CChefIoHb8iDN+TCq7hwB524Q05cwW5cwW56gl30BLtwBR0HetL7MWmtpBtySDfkkGHII92YR5ZxCFnGIVh0gzf1lJQB8L6HdD0Vjvcq0hDWK8ByBUKTWOH2jneORjAT7W40BPj0oPcNkc8OJgPoklIGv6KMygBCaDMQSTcjrdeD51Wk+z/Irh8jUv8KpiM+Bw1YrBHhK7KO+tI2b8gV6aG10x3ooDvQiTNoxxnooifYSZtvH+6Q84ATTF/QoEEIDeF/WhQUQKKgIKUSed83DBoTVm0yFl0yqfpMhlrKSNalk6RPP9ArTjVkxT2hctzwvoN0/Dwc/Sr5t5HsPmqi84FO1ARTCPERcLgxh9uklG/09rXDfHZoF7gvZQ6243rg+shbnxBiW29lBwiZQHu8jfia9LEN86NuyNfgODoOCU2Ct6EC+OBIhRK8DX1iILdhWF8LRk0wpZSnH8PXGoCCg94PBRoPKdMOpAohdJFe5uHKHGzHE8ATAEKI9X3teicqahsSA7UNiYHahsRgMLShLyRGBuD/8SZwqRDCGPGELQfWHlxAhiddlwEXRj66Cuitx6qioqKiotIvxEUwhRDnCSEagJnA2xHnHqSU24GXgB3Ae8D393vICiHeEULsX7B3K/BTIUQl4TnNJ2PdBhUVFRWV44u4OP1IKRcDi3vZdi9w72E+X3DQ6yrCS0+OlieO4TuJhtqGxEBtQ2KgtiExGAxtOCLHVaQfFRUVFRWVYyXR5jBVVFRUVFQSkkEnmEKIi4QQ24UQihBi6iHbfiWEqBRC7BZCHHaBnxCiWAjxmRCiQgjxohDCEBvLD0/Ehk2RvxohxKZeytUIIbZGyiVUdAYhxF1CiH0HtWNBL+XmR45NpRDil7G286sQQvxJCLFLCLFFCLFYCHHYyOqJeByO9LtGnOxejGz/TAhRFHsre0cIUSCEWCaE2Bm5tn98mDJzhBCOg86xO+Jh61dxpHNDhHkkchy2CCEmx8PO3hBCjDjo990khOgWQtx8SJmEPw5fCynloPojHJ92BLAcmHrQ56OBzYARKAb2AtrDfP8l4NLI68eBG+PdpoNsexC4o5dtNUBmvG3sxba7CEd0+qoy2sgxKQEMkWM1Ot62H2TfGYAu8vp+4P6BcBz68rsCNwGPR15fCrwYb7sPsS8PmBx5nQTsOUwb5gBvxdvWI7TjK88NYAHwLuG15icAn8Xb5iOcV83AsIF2HL7O36DrYUopd0opdx9m07eARVJKn5SyGqjkEMehSNi9ucArkY/+A5wbTXv7SsS2iwnH2h2MTAcqpZRVMhxIfxHhY5YQSCk/kP+LLvUp4fW/A4G+/K7fInyuQ/jcP00kUEoVKWWTlHJj5LUT2MngjO71LeBpGeZTwuvNEzXr+mnAXillbbwNiSWDTjC/giFA/UHvB1rYvVlAi5SyopftEvhACLEhEt0o0fhBZJjpX0KIwwXT7MvxSRSuIdwTOByJdhz68rseKBM59x2Er4WEIzJcPAn47DCbZwohNgsh3hVCjImpYX3jSOfGQLoGLqX3h/dEPw7HTKLFku0TiRJ2r7/oY3su46t7lydJKRuFENnAh0KIXVLKlf1ta298VRuAx4DfEf4tf0d4aPmaQ3dxmO/G1IW7L8dBCHEbEASe62U3cT0OhyFhz/ujRQhhA14FbpZSdh+yeSPh4cGeyBz564QDnyQSRzo3BspxMADnAL86zOaBcByOmQEpmDJBwu71F0dqjwin7Dgf6DXvlZSyMfJ/qxBiMeGhuJjdqPt6TIQQ/wDeOsymvhyfqNKH43AVcDZwmoxM2BxmH3E9DoehL7/r/jINkXMtBbDHxry+IYTQExbL56SUrx26/WABlVK+I4T4mxAiU0qZMPFN+3BuxP0a6CNnAhullC2HbhgIx+HrcDwNyQ7ksHunA7uklA2H2yiEsAohkva/JuygkjBB5g+ZhzmPw9u2DigXYS9lA+EhnzdjYV9fEELMJxxh6hwppbuXMol4HPryu75J+FyH8Lm/tLcHgngQmU99EtgppfxzL2Vy98+7CiGmE763dcTOyq+mj+fGm8DCiLfsCYBDStkUY1P7Qq+jXYl+HL428fY66u8/wjfkBsAHtADvH7TtNsIeg7uBMw/6/B0gP/K6hLCQVgIvA8YEaNO/gRsO+SwfeOcgmzdH/rYTHkKM+2uehdcAAAHDSURBVLE4yNZngK3AFsI3hbxD2xB5v4CwB+TeBGxDJeH5pU2Rv/1epQl/HA73uwJ3ExZ/AFPkXK+MnPsl8bb5EPtPJjw0ueWg338BcMP+6wL4QeQ330zYKevEeNt9SBsOe24c0gYBPBo5Tls5yMs/Uf4AC2EBTDnoswFzHL7unxrpR0VFRUVFpQ8cT0OyKioqKioqx4wqmCoqKioqKn1AFUwVFRUVFZU+oAqmioqKiopKH1AFU0VFRUVFpQ+ogqmioqKiotIHVMFUUVFRUVHpA6pgqqgcJwghpkUC4JsikWe2CyHGxtsuFZWBghq4QEXlOEIIcQ/hyD5moEFKeV+cTVJRGTCogqmichwRiSe7DvASDlsWirNJKioDBnVIVkXl+CIdsAFJhHuaKioqfUTtYaqoHEcIId4EFgHFhIPg/yDOJqmoDBgGZD5MFRWVo0cIsRAISimfF0JogdVCiLlSyqXxtk1FZSCg9jBVVFRUVFT6gDqHqaKioqKi0gdUwVRRUVFRUekDqmCqqKioqKj0AVUwVVRUVFRU+oAqmCoqKioqKn1AFUwVFRUVFZU+oAqmioqKiopKH1AFU0VFRUVFpQ/8P/RN/2/KNKjTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def scalar_field_contour(f,xmin,xmax,ymin,ymax,levels=None):\n",
    "\n",
    "    fv = np.vectorize(f)\n",
    "\n",
    "    X = np.arange(xmin, xmax, 0.1)\n",
    "    Y = np.arange(ymin, ymax, 0.1)\n",
    "    X, Y = np.meshgrid(X, Y)\n",
    "    \n",
    "    # https://stackoverflow.com/a/54088910/1704140\n",
    "    Z = fv(X,Y)\n",
    "    \n",
    "    fig, ax = plt.subplots()\n",
    "    CS = ax.contour(X, Y, Z,levels=levels)\n",
    "    ax.clabel(CS, inline=1, fontsize=10,fmt='%1.1f')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('y')\n",
    "    fig.set_size_inches(7,7)\n",
    "    \n",
    "scalar_field_contour(u,-10,10,-10,10,levels=[10,20,30,40,50,60])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4 Connecting energy and forces with the gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.5 Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Plot the cross-section of $h(x,y) = e^y\\sin(x)$ where $y=1$.  Plot the cross section of $h(x,y)$ where $x=\\pi/6$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_function(f,xmin,xmax,color=None):\n",
    "    ts = np.linspace(xmin,xmax,1000)\n",
    "    plt.plot(ts,[f(t) for t in ts],c=color)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from math import pi, e, sin\n",
    "plot_function(lambda x: e*sin(x),-pi,pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "plot_function(lambda y: math.exp(y)/2,-3,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
